THE INDIAN ENGINEERING COLLEGE
VADAKKANGULAM
ELECTRICAL AND ELECTRONICS DEPARTMENT
2 MARK QUESTIONS AND ANSWERS
EE 34-ELECTROMAGNETIC THEORY
UNIT I
1. State stokes theorem.
The line integral of a vector around a closed path is equal to the surface integral of the
normal component of its curl over any surface bounded by the path
H.dl = (▼xH)ds
2. Define divergence.
The divergence of a vector F at any point is defined as the limit of its surface integral
per unit volume as the volume enclosed by the surface around the point shrinks to zero.
3. State Divergence Theorem.
The integral of the divergence of a vector over a volume v is equal to the surface
integral o f the normal component of the vector over the surface bounded by the volume.
4. What is the physical significance of div D ?
▼•D= ρv
The divergence of a vector flux density is electric flux per unit volume leaving a
small volume. This is equal to the volume charge density.
5. State the condition for the vector F to be solenoidal.
▼• F =0
6. State the condition for the vector F to be irrotational.
▼x F =0
7. Describe what are the sources of electric field and magnetic field?
Stationary charges produce electric field that are constant in time, hence the term
electrostatics. Moving charges produce magnetic fields hence the term magnetostatics.
8. State coulombs law.
Coulombs law states that the force between any two point charges is directly
proportional to the product of their magnitudes and inversely proportional to the square
of the distance between them. It is directed along the line joining the two charges.
F=Q1Q2/ 4 πεr2
9. Define potential difference.
Potential difference is defined as the work done in moving a unit positive charge
from one point to another point in an electric field.
10. Define potential.
Potential at any point is defined as the work done in moving a unit positive charge
from infinity to that point in an electric field.
V=Q / 4 πεr
11. State the principle of superposition of fields.
The total electric field at a point is the algebraic sum of the individual electric field at
that point.
12. What is a point charge?
Point charge is one whose maximum dimension is very small in comparison with any
other length.
13. Define linear charge density.
It is the charge per unit length.
14. Define surface charge density.
It is the charge per surface area.
15. Define Biot –Savart Law?
The magnetic flux density produced by a current element at any point in a
magnetic field is proportional to the current element and inversely proportional to the square
of the distance between them.
16. What is a Scalar quantity?
A Quantity which has magnitude only is called Scalar quantity. It is represented by
length. EG: Temperature, Mass, Volume and Energy.
17. What is a Vector quantity?
A Quantity which has both magnitude and direction is called Vector quantity. It is
graphically represented by a line with an arrow to show magnitude and direction.EG: Force,
Velocity, and Acceleration
18. Define Unit Vector?
A Vector which has magnitude unity and defining the same direction as given vector.
19. Give the properties of Vectors.
1) Vector addition obeys commutative law A +Β = B +A
2) Vector addition obeys associative law A + (B +C) = (A + B) + C
3) - A is also a vector. It has same magnitude; its direction is 1800 away from direction
of A. A – B = A + (- B)
20. Define Scalar or Dot Product.
A.B = ABcos Φ 0≤ Φ ≤ Π where A = A and B = B and Φ angle between
two vectors. It is denoted as A.B It is the product of magnitudes of A and B and the
cosine of the angle between them.
21. Define Cross or Vector product.
It is denoted as A ҳ B.It is a vector whose magnitude is equal to the product of
magnitudes of two vectors multiplied by the sine angle between them and direction
perpendicular to plane containing A and B.
UNIT II
1. State Gauss law for electric fields
The total electric flux passing through any closed surface is equal to the total charge
enclosed
by that surface.
2. Define electric flux.
The lines of electric force is electric flux.
3. Define electric flux density.
Electric flux density is defined as electric flux per unit area.
4. Define electric field intensity.
Electric field intensity is defined as the electric force per unit positive charge.
E =F/ Q =Q/4 πεr2 V/m
5. Name few applications of Gauss law in electrostatics.
Gauss law is applied to find the electric field intensity from a closed surface. e.g. Electric
field can be determined for shell, two concentric shell or cylinders
6. State Gauss law for magnetic field.
The total magnetic flux passing through any closed surface is equal to zero. B.ds =0
7. Give the expression for electric field intensity due to a single shell of charge
E = Q / 4 πεr 2
8. Give the expression for potential between two spherical shells
V= 1/ 4 πε(Q1/a – Q2/b)
9. Give the relationship between potential gradiant and electric field.
E= - ▼V
10. What is electrostatic force?
The force between any two particles due to existing charges is known as electrostatic
force, repulsive for like and attractive for unlike.
11. What are dielectrics?
Dielectrics are materials that may not conduct electricity through it but on applying
electric field induced charges are produced on its faces. The valence electrons in atoms of a
dielectric are tightly bound to their nucleus.
12. What is a capacitor?
A capacitor is an electrical device composed of two conductors which are separated
through a dielectric medium and which can store equal and opposite charges ,independent of
whether other conductors in the system are charged or not.
13. Define dielectric strength.
The dielectric strength of a dielectric is defined as the maximum value of electric field
that can b applied to the dielectric without its electric breakdown.
14. What meaning would you give to the capacitance of a single conductor?
A single conductor also possess capacitance. It is a capacitor whose one plate is at
infinity.
15. Why water has much greater dielectric constant than mica.?
Water has a much greater dielectric constant than mica, because water has a
permanent dipole moment, while mica does not have.
16. Write down the expression for capacitance between two parallel plates.
C=εA / d
17. What is meant by displacement current?
Displacement current is nothing but the current flowing through capacitor.
J= D / t
18. Write the boundary conditions at the interface between two perfect dielectrics.
i)The tangential component of electric field is continuous
i.e)Et1=Et2
ii)The normal component of electric flux density is continuous
i.e)Dn1=Dn2
19. Explain the conservative property of electric field.
The work done in moving a point charge around a closed path in a electric field is
zero. Such a field is said to be conservative.
E.dl = 0
20. What are equipotential surfaces?
An equipotential surface is a surface in which the potential energy at every point is of the
same value
UNIT III
1. Write poisson’s and laplace ’s equations.
Poisson ‘s eqn:
▼2V= - ρv / ε
Laplace’ s eqn:
▼2V= 0
2. What are the significant physical differences between Poisson ‘s and laplace ‘s equations.
Poisson ‘s and laplace ‘s equations are useful for determining the electrostatic
potential V in regions whose boundaries are known. When the region of interest contains
charges poissons equation can be used to find the potential. When the region is free from
charge laplace equation is used to find the potential.
3. Define magnetic field strength.
The magnetic field strength (H) is a vector having the same direction as magnetic flux
density. H=B/μ
4. Write down the expression for magnetic field at the centre of the circular coil.
H = I/2a.
5. Write he expression for field intensity due to a toroid carrying a filamentary current I
H=NI / 2ïR
6. Give the relation between magnetic flux density and magnetic field intensity.
B =μ H
7. Define inductance.
The inductance of a conductor is defined as the ratio of the linking magnetic flux to the
current producing the flux. L = Nφ / I
8. Give the formula to find the force between two parallel current carrying conductors.
F=μI 1I2/ 2πR
9. Give the expression for torque experienced by a current carrying loop situated in a
magnetic field.
T = I A B sinθ
10. What is torque on a solenoid?
T = N I ABsin θ
11. Write the expression for energy density in electrostatic field.
W=1 / 2 εE2
12. What is the expression for energy stored in a magnetic field?
W = ½ LI2
13. What is energy density in magnetic field?
W = ½ μH2
14. Distinguish between solenoid and toroid.
Solenoid is a cylindrically shaped coil consisting of a large number of closely spaced
turns of insulated wire wound usually on a non magnetic frame. If a long slender solenoid
is bent into the form of a ring and there by closed on itself it becomes a toroid.
15. What is lorentz force?
Lorentz force is the force experienced by the test charge .It is maximum if the
direction of movement of charge is perpendicular to the orientation of field lines.
16. State Biot –Savarts law.
It states that the magnetic flux density at any point due to current element is
proportional to the current element and sine of the angle between the elemental length
and inversely proportional to the square of the distance between them
dB =μ Idl sinθ / 4πr2
17. State amperes circuital law.
Magnetic field intensity around a closed path is equal to the current enclosed by the path.
H • dl=I
18. Give the force on a current element.
dF = B I dl sinθ
19. Define magnetic vector potential.
It is defined as that quantity whose curl gives the magnetic flux density.
B=▼ x A=μ / 4πJ/r dv web/m2
20. Define magnetic moment.
Magnetic moment is defined as the maximum torque per magnetic induction of
flux density. m=IA
21. Give the relation between electric field intensity and electric flux density.
D=Eε C/m2
22. Define current density.
Current density is defined as the current per unit area.
J= I/A Amp/m2
23. Define self inductance.
Self inductance is defined as the rate of total magnetic flux linkage to the current through
the
coil.
24. Define magnetic moment.
Magnetic moment is defined as the maximum torque on the loop per unit magnetic
induction.
25. Write the point form of continuity equation and explain its significance.
▼•J= - ρv / ε
26. State point form of ohms law.
Point form of ohms law states that the field strength within a conductor is proportional to
the current density.
J= σE
27. Write down the magnetic boundary conditions.
i) The normal components of flux density B is continuous across the boundary.
ii) The tangential component of field intensity is continuous across the boundary.
UNIT IV
1. State Maxwells fourth equation.
The net magnetic flux emerging through any closed surface is zero.
2. State Maxwells Third equation
The total electric displacement through the surface enclosing a volume is equal to the
total
charge within the volume.
3. Define ohms law at a point
Ohms law at appoint states that the field strength within a conductor is
proportional to current density.
4. State electric displacement.
The electric flux or electric displacement through a closed surface is equal to the charge
enclosed by the surface.
5. What is displacement flux density?
The electric displacement per unit area is known as electric displacement density or
electric
flux density.
6. What is the significance of displacement current?
The concept of displacement current was introduced to justify the production of magnetic
field in empty space. It signifies that a changing electric field induces a magnetic field .In empty
space the conduction current is zero and the magnetic fields are entirely due to displacement
current.
7. State Poyntings Theorem.
The net power flowing out of a given volume is equal to the time rate of decrease of the
the energy stored within the volume- conduction losses.
8. Define poynting vector.
The vector product of electric field intensity and magnetic field intensity at a point is a
measure of the rate of energy flow per unit area at that point. P =E X H
9. What is an emf?
An electro-motive force is a voltage that arises from conductors moving in a
magnetic field or from changing magnetic fields.
10. State Faraday’s law.
Faraday’s law states that, the total emf induced in a closed circuit is equal to the
time rate of decrease of the total magnetic flux linking the circuit.
11. State Lenz’s law.
The Lenz’s law states that, the induced current in the loop is always in such a
direction as to produce flux opposing the change in flux density.
12. Explain briefly the different types of emf’s produced in a conductor placed in a
magnetic field.
There are two ways in which we can induce emf in a conductor. If a moving
conductor is placed in a static magnetic field then the emf produced in the conductor is called
dynamically induced emf. If the stationary conductor is placed in a time varying magnetic
field, then the emf produced is called statically induced emf.
13. Give the Maxwell’s equation – I in both integral form and point form.
Maxwell’s equation – I is derived from the Ampere’s circuital law which states
that the line integral of magnetic field intensity H on any closed path is equal to the current
enclosed by that path.
Maxwell’s equation – I in integral form is
Maxwell’s equation – I in point form is
The magneto motive force around a closed path is equal to the sum of the
conduction current and displacement current enclosed by the path.
14. Give the Maxwell’s equation – II in both integral form and point form.
Maxwell’s equation – II is derived from Faraday’s law which states that the emf
induced in a circuit is equal to the rate of decrease of the magnetic flux linkage in the circuit.
Maxwell’s equation - II in integral form is
Maxwell’s equation – II in point form is
The electro motive force around a closed path is equal to the magnetic
displacement (flux density) through that closed path.
15. Give the Maxwell’s equation – III in both integral form and point form.
The Maxwell’s equation – III is derived from electric Gauss’s law which states
that the electric flux through any closed surface is equal to the charge enclosed by the
surface.
Maxwell’s equation – III in integral form is
Maxwell’s equation – III in point form is
The total electric displacement through the surface enclosing a volume is equal to
the total charge within the volume.
16. Give the Maxwell’s equation – IV in integral form.
Maxwell’s equation – IV is derived from magnetic Gauss’s law which states that,
the total magnetic flux through any closed surface is equal to zero.
Maxwell’s equation – IV in integral form is
17. Give the Maxwell’s equation – IV in point form.
Maxwell’s equation – IV in point form is
The net magnetic flux emerging through any closed surface is zero.
18. Distinguish between the conduction current and displacement current.
Conduction current Ic is flowing through a conductor having resistance R, when
potential V is applied across the conductor.
Displacement current ID is flowing through a capacitor when ac voltage is applied
across the capacitor.
dt
19. What is Eddy current and Eddy current loss?
In electrical machines, the alternating magnetic fields induce emf in the cores also
apart from the coil. This small amount of emf induced in the core circulates current in the
core. This current is called eddy current and the power loss, which appears in the form of
heat, due to these eddy currents is called eddy current loss.
20. What is main cause of eddy current?
The main cause of eddy current is that it produces ohmic power loss and causes local
heating
UNIT V
1. Define a wave.
If a physical phenomenon that occurs at one place at a given time is reproduced at other
places at later times , the time delay being proportional to the space separation from the first
location then the group of phenomena constitutes a wave.
2. Mention the properties of uniform plane wave.
i) At every point in space ,the electric field E and magnetic field H are perpendicular to
each other.
ii)The fields vary harmonically with time and at the same frequency everywhere in
space.
3. Define intrinsic impedance or characteristic impedance.
It is the ratio of electric field to magnetic field.or It is the ratio of square root of
permeability to permittivity of medium.
4. Give the characteristic impedance of free space.
377ohms
5. Define skin depth
It is defined as that depth in which the wave has been attenuated to 1/e or approximately
37% of its original value.
6. What is the effect of permittivity on the force between two charges?
Increase in permittivity of the medium tends to decrease the force between two charges
and decrease in permittivity of the medium tends to increase the force between two charges.
7. Define loss tangent.
Loss tangent is the ratio of the magnitude of conduction current density to displacement
current density of the medium.
8. Define reflection and transmission coefficients.
Reflection coefficient is defined as the ratio of the magnitude of the reflected field to that
of the incident field.
9. Define transmission coefficients.
Transmission coefficient is defined as the ratio of the magnitude of the transmitted field
to that of incident field.
10. How can the eddy current losses be eliminated?
The eddy current losses can be eliminated by providing laminations. It can be proved that
the total eddy current power loss decreases as the number of laminations increases.
11. What is the fundamental difference between static electric and magnetic field lines?
There is a fundamental difference between static electric and magnetic field lines The
tubes of electric flux originate and terminates on charges, whereas magnetic flux tubes are
continuous.
12. What are uniform plane waves?
Electromagnetic waves which consist of electric and magnetic fields that are
perpendicular to each other and to the direction of propagation and are uniform in plane
perpendicular to the direction of propagation are known as uniform plane waves.
13. Write short notes on imperfect dielectrics.
A material is classified as an imperfect dielectrics when conduction current density is
small in magnitude compared to the displacement current density.
14. What is the significant feature of wave propagation in an imperfect dielectric?
The only significant feature of wave propagation in an imperfect dielectric compared to
that
in a perfect dielectric is the attenuation undergone by the wave.
15. Give the wave equation in terms of electric field and magnetic field.
The electromagnetic wave equation in terms of electric field is,
The electromagnetic wave equation in terms of magnetic field is,
6. Give the wave equation in free space.
The wave equation in free space in terms of electric field is,
The wave equation in free space in terms of magnetic field is,
17. List out the properties of a uniform plane wave.
If the plane of wave is the same for all points on a plane surface, it is called plane
wave. If the amplitude is also constant in a plane wave, it is called uniform plane wave. The
properties of uniform plane waves are:
a) At every point in space, E and H are perpendicular to each other and to the
direction of travel.
b) The fields vary with time at the same frequency, everywhere in space.
c) Each field has the same direction, magnitudes and phase at every point in
any plane perpendicular to the direction of wave travel.
18. Give the expression for the characteristic impedance of the wave.
The characteristic impedance or intrinsic impedance is the ratio of the electric
field intensity to the magnetic field intensity.
19. What is Vector Helmholtz equation.
The wave equation in lossless medium in phasor form is called the vector
Helmholtz equation.
20. Give the wave equation for a conducting medium.
The wave equation for a conducting medium in phasor form is given as,
21. What is skin effect and skin depth?
In a good conductor the wave is attenuated as it progresses. At higher frequencies
the rate of attenuation is very large, and the wave may penetrate only a very short distance
before being reduced to a small value. This effect is called skin effect.
The skin depth is defined as that depth in which the wave has been attenuated
to 1/e or approximately 37% of its original value. It is also known as depth of penetration.
where
is the attenuation constant,
22. Give the expression for attenuation constant and phase shift constant for a wave
propagating in a conducting medium.
The attenuation constant for a wave propagating in a conducting medium is,
The phase shift constant for a wave propagating in a conducting medium is,
23. Give the expression for the velocity of propagation of a wave in any medium.
The velocity of propagation of a wave in any medium is,
. 16 MARKS
UNIT I
PART B
1. (i) Explain the electric field distribution inside and outside a conductor
(ii) Explain the principle of electrostatic shielding.
(iii) Draw the equipotent lines and E lines inside and around a metal sphere.
2.
i) State and prove Divergence theorem.
ii) State and prove Stokes theorem.
3. Given A = ax + ay, B = ax + 2az and C = 2 ay + az . Find (A X B) X C and compare
it with A X (B X C). Using the above vectors, find A.B X C and compare it with
A X B.C.
4. Find the value of the constant a, b, c so that the vector E = (x + 2y + az) ax +
(bx – 3y –2) ay + (4x + cy + 2z) az is irrotational.
5. Using the Divergence theory, evaluate ∫∫ E.ds = 4xz ax – y2 ay + yz az over the cube bounded by x = 0;
x = 1; y = 0; y = 1; z = 0; z = 1.
6. Explain the spherical co-ordinate system?
7. (i) Use the cylindrical coordinate system to find the area of the curved surface of a
right circular cylinder where r = 20 m, h = 5m and 30º    120 º.
(ii)State and explain Divergence theorem.
8. (i) Derive the stoke’s theorem and give any one application of the theorem in electromagnetic
fields
(ii)Obtain the spherical coordinates of 10ax at the point P (x = -3, y = 2, z = 4).
9. Find the charge in the volume
0  x  2m
0  y  2m
0  z  2m
If ρ = 10 x2 y z μC/m3.
10. (i) Determine the constant c such that the vector F = (x + ay)i + (y + bz)j +
(x + cz)k will be solenoidal.
(ii) Given A  2r cos  I r  r I in cylindrical co-ordinate. For the contour shown
in Fig.Q-32, verify Stoke’s theorm.
Fig.Q-32.
11. Verify Stoke’s theorem for a vector field F = ρ2cos2 Φaρ+zsinΦaz around the
path L defined by 0≤ ρ ≤ 3, 0≤ Φ ≤ 45o and z = 0.
12. i) What are the major sources of Electromagnetic fields (any five)?
ii) What are the positive and negativeeffcts of EM fields on living things?
iii) What are the E and H field limits for public exposure?
iv)Give any one example to reduce the effect of EM field.
13. Verify the divergence theorem for a vector field A = xy2
ax+y3 ay+y2z az
and
the surface is a cuboid defined by 0<x<1, 0<y<1, 0<z<1.
14. Given that F = x2 y ax - yay. Find ∫ F. dl
for the closed path shown in figure
and also verify Stoke’s theorem.
15. i) Given A = 5ax and B = 4ax + t ay ; Find ‘t’ such that the angle between A and
B is 45˚
ii) Using the Divergence theorem, evaluate ∫∫ A.dS = 2xy ax + y2 ay + 4yz az over the
cube bounded by x = 0; x = 1; y = 0; y = 1; z = 0; z = 1.
16. i) Determine divergence and curl of the vector A = x2 ax + y2 ay + y2 az.
ii) Determine the gradient of the scalar field at P (√2, π / 2, 5) defined in
cylindrical co-ordinate system as A= 25ρ sinφ.
17. a) Determine divergence and Curl of the following vector fields.
i) P= x2yz ax + xz az.
ii) Q = ρsinΦaρ + ρ2z aΦ + zcosΦ az
iii) T = 1 / r2 cosθ ar + r sinθ cosθ aθ+ cosθ aΦ
b) Fnd the gradient of the following scalar fields
i) V = e-z sin2x coshy
ii) U = ρ2z cos 2Φ
iii) W = 10r sin2θ cosΦ.
18. i) Show that the vector field A is conservative if A possesses one of the following
two properties. 1) The line integral of the tangential component of A along a
path extending from point P to point Q is independent of the path.2) The line
integral of the tangential component of A along a closed path s zero.
ii) If A = ρcosΦaρ + sinΦaΦ , evaluate ∫ A.dl around the path shown in figure.
Confirm this using Stoke’s theorem.
19. i) A vector field is given by the expression F = (1/ρ ) aρ in cylindrical
co-ordinates and F = (1/r) ar in spherical co-ordinates. Determine F in each case
in the Cartesian form at a point (1, 1, 1).
ii) If a scalar potential is given by the expression Φ = xyz, determine the potential
gradient and also prove that vector F = grad Φ is irrotational.
20. i) Given two points A (2, 3,-1) and B (4, 25˚, 120˚). Find the spherical and
cylindrical co- ordinates of point A and Cartesian and cylindrical co-ordinates
of point B.
ii) Find the curl of H at P (2, Π/6, 0), where H = 2ρ cosφ aρ - 4ρ sinφ aφ + 3az.
UNIT II
PART B
1. State and explain the experimental law of coulomb?
2. State and prove Gauss’ law and write about the applications of Gauss law?
3. State and explain Gauss’s law. Derive an expression for the potential at a point outside a
hollow sphere having a uniform charge density
4. (i) A circular disc of radius ‘a’, m is charged uniformly with a charge density of σ C/m2
Find the electric field intensity at a point ‘h’, m from the disc along its axis.
(ii) A circular disc of 10 cm radius is charged uniformly with a total charge of 10-6c.
Find the electric intensity at a point 30 cm away from the disc along the axis.
5. A line charge of uniform density q C / m extends from the point (0, -a) to the point (0, 1)
in the x-y plane. Determine the electric field intensity E at the point (a, 0).
6. Define the electric potential, show that in an electric field, the potential difference
b
between two points a and b along the path, Va – Vb = -
 E.dl
a
7. What is dipole moment? Obtain expression for the potential and field due to an electric
dipole.Two point charges Q1 = 4nC1, Q = 2nC are kept at (2, 0, 0) and (6, 0, 0).Express
the electric field at (4, -1, 2)
8. Derive the electric field and potential distribution and the capacitance per unit
length of a coaxial cable.
9. Explain in detail the behavior of a dielectric medium in electric field.
10. i)Discuss Electric field in free space, dielectric and in conductor.
ii) Determine the electric field intensity at P ( -0.2,0,-2.3) due to a point charge of
5 nC at (0.2, 0.1, -2.5) in air.
11.(i) Derive the electrostatic boundary conditions at the interface of two deictic media.
(ii) If a conductor replaces the second dielectric, what will be the potential and electric
field inside and outside the conductor?
12. (i) Derive the expression for scalar potential due to a point charge and a ring charge.
(ii) A total charge of 100 nC is uniformly distributed around a circular ring of 1.0m
radius. Find the potential at a point on the axis 5.0 m above the plane of the ring.
Compare with the result where all charges are at the origin in the form of a point
charge.
13. (i) Derive the expression for energy density in electrostatic fields.
(ii) A capacitor consists of squared two metal plates each 100 cm side placed parallel and 2 mm apart.
The space between the plates is filled with a dielectric having a relative permittivity of 3.5. A
potential drop of 500 V is maintained between the plates. Calculate i) the capacitance, ii) the
charge of capacitor, iii) the electric flux density, iv) the potential gradient
14. A uniformly distributed line charge, 2m long, with a total charge of 4 nC is in
alignment with z axis, the mid point of the line being 2 m above the origin. Find the
electric field E at a point along X axis 2 m away from the origin. Repeat for
concentrated charge of 4 nC on the z axis 2 m from the origin, compare the results.
15. (i) Define the potential difference and absolute potential. Give the relation between
potential and field intensity.
(ii) Two point charges of +1C each are situated at (1, 0, 0) m and (-1, 0, 0) m. At what
point along Y axis should a charge of -0.5 C be placed in order that the electric
field E = 0 at (0, 1, 0) m?
16. If V = [2 x2y + 20z – 4 / (x2 + y2)] volts, find E and D at P (6,-2.5, 3).
17. Derive an expression for capacitance of a spherical capacitor with conducting shells
Of radius ‘a’ and ‘b’.
18. Obtain an expression for energy stored and and energy density in a capacitor.
19. Conducting spherical shells with radii a = 10 cm and b= 30 cm are maintained at
potential difference of 100 V such that V(r = b) = 0 and V(r = a) = 100 V. Determine
V and E in region between shells.
20. A total charge of 10-8 C is distributed uniformly along a ring of radius 5m. Calculate
the potential on the axis of the ring at a point 5m from the centre of the ring.
21. Two parallel plates with uniform surface charge densities equal and opposite to each
other have an area of 2 m2 and distance of separation of 2.5 mm in free space. A
steady potential of 200 V is applied across the capacitor formed. If a dielectric of
width 1 mm and relative permittivity 2 is inserted into this arrangement what is the
new capacitance formed?
22. i) Derive Poisson’s and Laplace’s equation and explain their significance in field
theory.
ii) Three concentrated charges of 0.25 μC are located at the vertices of an equilateral
triangle of 10 cm side. Find the magnitude and direction of the force one charge
due to the other two charges.
23. A positive charge Q is located at the centre of a spherical conducting shell of inner
radius Ri and outer radius Ro. Determine E and V as function of radial distance R.
24. i) Write a note on dielectrics.
ii) Find the electric field intensity at the point (0, 0, 5) m due to Q1 = 0.35μC at
(0, 4, 0) and q2 =-0.55 μC at (3, 0, 0) m.
25. The electric flux density is given as D= r/4 ar nC / m2 in free space. Calaculate E
at r = 0.25 m, the total charge within the sphere of r = 0.25m and the total flux
leaving the sphere of r = 0.35m.
26. An infinitely long uniform line charge is located at y=3, z=5. If ρL= 30 nC/m. Find
field intensity E at: i) origin ii) P (0, 6,) and iii) Q (5, 6, 1).
UNIT III
PART B
1. (i) Use Biot – Savart’s law to find magnetic field intensity for finite length of
conductor at a point P on Y – axis.
(ii)A steady current of ‘I’ flows in a conductor bent in the form of a square
loop of side ‘a’. Find the magnetic field intensity at the centre of the
current loop.
iii) Find the magnetic field intensity at the centre of a square of sides equal to 5m
and carrying 10 A current.
2. (i) when a current carrying wire is placed in an uniform magnetic field,
show that torque acting on it is T= m X B
(ii) A magnetic circuit comprising a toroid of 5000 turns and an area of 6cm2
and mean radius of 15 cm carries a current of 4A. Find the reluctance
and flux given μr = 1.
3. Calculate B due to a long solenoid and a thin toroid.
4. (i) Derive for force and torque in a magnetic field using motor as an example.
(ii) Find the torque about the y axis for the two conductors of length l, carrying
current in opposite directions, separated by a fixed distance w, in the uniform
magnetic field in x direction.
5. (i) Explain magnetization in magnetic materials and explain how the effect of
magnetization is taken into account in the calculation of B/H.
(ii) Find H in a magnetic material
a. When µ = 0.000018 H/m and H = 120 A/m.
b. When B = 300 µT and magnetic susceptibility = 20.
6. a) Derive the magnetic force between two parallel conductors carrying equal
current in the (i) Same direction
(ii) opposite direction
b) Two wires carrying currents in the same direction of 5000 A and 10000 A are
placed with their axes 5 cm apart. Calculate the force between them.
7. (i) Find the field intensity at a point due to a straight conductor carrying current I
as shown in Fig.Q-7.
Fig.Q-7
(ii) Find H at the centre of an equilateral triangular loop of side 4 m carrying
current of 5 A.
8. (i) Derive the expression for co-efficient of coupling in terms of mutual and self
inductances.
(ii) An iron ring with a cross sectional area of 3 cm2 and a mean circumference of
15 cm is wound with 250 turns wire carrying a current of 0.3 A. The relative
permeability of the ring is 1500. Calculate the flux established in the ring.
If a saw cut of width 2mm is made in the above ring, find the new value of flux
in the circuit.
9. Develop an expression for magnetic field intensity inside and outside a solid
cylindrical conductor of radius ‘a’, carrying a current I with uniform density.
Sketch the variation of the field intensity.
10. Derive H due to a circular current loop and extend the same to compute H due to a
long solenoid.
11. i)State and prove Ampere’s circuital law.
ii) State and explain Biot- Savart’s law
12. i) Obtain an expression for magnetic vector potential.
ii) Give a brief note on magnetic materials.
13. At a point P (x,y,z) the components of vector magnetic potential A are given as
Ax = (4x + 3y+2z); Ay = (5x + 6y +3z) and Az = (2x + 3y +5z). Determine B at
point P.
14. Derive the boundary conditions between two magnetic media.
15. A solenoid has an inductance of 20 mH. If the length of the solenoid is increased by
two times and the radius is decreased to half of its original value, find the new
inductance.
16. Write short notes on Magnetic vector potential, Biot- Savart’s law, Lorentz law of
force and Magnetic energy density.
17. An iron ring with a cross sectional area of 8 cm2 and a mean circumference of
120 cm is wound with 480 turns wire carrying a current of 2 A. The relative
permeability of the ring is 1250. Calculate the flux established in the ring.
18. A uniform cylindrical coil of 2000 turns is 60 m long and 5 cm diameter. If the coil
carries a current of 10 mA, find the magnetic flux density at the centre of the coil, on
the axis at one end of the coil and on the axis halfway between centre and one end of
the coil.
19. A circular loop located on x2 + y2 = 9, z=0 carries a direct current of 10 A along aΦ.
Determine H at (0, 0, 4) and (0, 0, -4).
20. A small current loop L1 with magnetic moment 5 az Am2 is located at the origin
while another small loop current L2 with magnetic moment 3 ay Am2 is located at
(4, -3, 10). Determine the torque on L2.
21. i) Find the maximum torque on an 85 turns, rectangular coil with dimension
(0.2 x 0.30) m, carrying current of 5A in a field B= 6.5 T
ii) Derive an expression for magnetic vector potential.
22. i) Derive an expression for the inductance of solenoid.
ii) Derive the boundary conditions at an interface between two magnetic media.
23. Determine the force per unit length between two long parallel wires A and B
separated by 5 cm in air and carrying currents of 40 A in the same direction and inthe
opposite direction.
24. Derive the expression for curl H = J.
25. Explain the concepts of scalar and vector magnetic potential.
UNIT IV
PART B
1. (i) Summarize Maxwell’s equation for time varying fields in integral and
differential form.
(ii) Compare the magnitude of conduction current density and displacement
current density in a good conductor in which σ = 107 S/m, Єr = 1 when
E = 1sin 120πt. Comment on the result.
2. (i) Derive Maxwell’s equation for   E and   H.
(ii) Explain (a) Motional emf. (b) Transformer emf.
3. Explain the different methods of emf induction with necessary governing
equations and with suitable examples.
4. (i) Write short notes on Faradays laws of electromagnetic induction.
(ii) What do you by displacement current? Write down the expression for the total
current density.
5. Explain the relationship between the field theory and circuit theory using a simple
RLC series circuit. Also explain the limitations of the circuit theory.
6. i) A straight conductor of length 40 cm moves perpendicularly to its axis at a velocity
of 50 m/s in a uniform magnetic field of flux density 1.2 T. Evaluate the emf
induced in the conductor if the direction of motion is
-
normal to the field
parallel to the field
at an angle 60o to the orientation of the field.
ii) A circular cross section conductor of radius 2mm carries a current ic = 2.5 sin
(5x 108t) µA.What is the amplitude of displacement current density if
σ = 35 MS/m and εr = 1.
7. Differentiate conduction and displacement current and derive the same .Explain the
need of displacement current in Maxwell’s equations.
8. i) Do the fields E = Em sinx sint ay and H = Em/μo cos x cos t ay , satisfy Maxwell’s
equations.
ii) Find the amplitude of displacement current density in the air near car antenna
where the field strength of EM signal E = 80 cos (6.277 x 108 t – 2.092 y ) az V/m.
9. From the fundamental laws , derive the Maxwell’s equations and the need for the
Maxwell’s contributions in both differential and integral form.
10.i) Discuss the relation between field theory and circuit theory. (8)
ii) In free space H = 0.2 cos (ωt – βx ) az A/ m. Find the total power passing through
a circular disc of radius 5 cm.
11. State and explain Faraday’s law of electromagnetic induction. Hence derive the
expressions for statically and dynamically induced emfs.
12. A circular loop of N turns of conducting wire lies in the xy – plane with its centre at
the origin of a magnetic field specified by B = Bo cos (πr / 2b ) sin ωt where ‘b’ is
the radius of the loop and ω is the angular frequency. Find the mf induce din the
loop.
13. i ) derive modified form of Ampere’s circuital law in intehral and differential forms,
ii) Find the amplitude of displacement current density inside a capacitor where
εr = 600 and D = 3 x 10-6 (sin ( 6 x 106 t – 0.3464x ) az C/m2 .
14. i) A square coil loop area 0.01 m2 and 50 turns is rotated about its axis at right
angles to a uniform magnetic field B = 1 T. Calculate the instantaneous value of
EMF induced in the coil when its plane is at right angles to the field, at 45 deg to
the field and in the plane of the field. Speed of rotation is 1000 rpm.
ii) A conducting cylinder of radius 5 cm, height 20 cm rotates at 600 rev / sec in a
radial field B = 0.5 T. Sliding contacts at the top and bottom are connected to
Voltmeter. Find the induced voltage.
15. What is displacement current? Show that the displacement current in the dielectric
Parallel plate capacitor is equal to the conduction current in the leads.
13. i) The conduction current flowing through a wire with conductivity σ = 3 x 107 S/m
and εr =1 is given by Ic = 3 sin ωt mA. If ω = 108 rad / sec. Find the displacement
current.
ii) The magnetic field intensity in free space is given as H = Ho sinθ ay A/m, where
θ = ωt = βz and β is a constant. Determine the current density vector J.
UNIT V
PART B
1. (i)Discuss the parameters :  ,  ,  , ,  ,  , Vphase and V group.
ii) Define Brewster angle and discuss the Brewster angle and degree of
polarization.
3. What is Poynting vector? Explain. Derive pointing theorem.
3. (i) Explain when and how an electromagnetic wave is generated.
(ii) Derive the electromagnetic wave equations in free space and mention the types
of solutions.
4. A plane wave propagating through a medium with µr=2, εr=8 has
E = 0.5 sin (108 t-βz)az (V/m). Determine (i) β (ii) The loss tangent (iii) wave
Impedance (iv) wave velocity (v) H field
5. A plane traveling wave has a peak electric field intensity E as 6 kV/m. If the
medium is lossless with µr=1, εr=3, find the velocity of the EM wave , peak
POYNTING vector, impedance of the medium and the peak value of the magnetic
field H. Derive all the formulae used.
6. Determine the amplitude of the reflected ad transmitted E and H at the interface of
two media with the following properties. Medium 1: µr=1, εr=8.5,σ = 1.
Medium 2: free space. Assume normal incidence and the amplitude of E in the
medium 1 at the interface is 1.5 mV/m. Derive all the formulae used.
7. (i) Derive the electromagnetic wave equation in frequency domain and the
propagation constant and intrinsic impedance.
(ii) Explain the propagation of EM waves inside the conductor.
8. Define and derive skin depth. Calculate skin depth for a medium with conductivity
100 mho/m, µr=2, εr=3 at 50Hz, 1MHz and 1 GHz.
9. In free space E (z,t) = 100 cos (wt-bz)ax(V/m). Calculate H and plot E and H
waveforms at t=0.
10. Derive the transmission and reflection coefficients at the interface of two media
for normal incidence. Discuss the above for an open and a short circuited line.
11. A free space –silver interface has E (incident) = 100 V/m in the free space side.
The frequency is 15 MHz and the silver constants are µr=1, εr=1, σ=61.7 MS/m.
Determine E (reflected), E (transmitted) at the interface.
12. Calculate intrinsic impedance η, propagation constant γ and wave velocity υ for a
conducting medium in which σ = 58 S / m, µr=1, εr=1 at a frequency of 100 MHz.