GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY
Electromagnetic Field Theory
(4th Semester)
QUESTION BANK
(Based on Numericals)
1. A boundary exists at z=0 between two dielectrics, 𝜀𝑟1 =2.5 region z<0 and
𝜀𝑟2 =4 region z>0. The field in region 𝜀𝑟1 is
𝐸⃗1 = −30𝑥̂50𝑦̂ + 70𝑧̂ V/m
Find
(a) Normal component of 𝐸⃗1
(b) Tangential component of 𝐸⃗1
(c) The angle 𝛼1 <=90 degree between 𝐸⃗1 and normal to surface
(d) Normal component of 𝐷2
(e) Tangential component of 𝐷2
(f) Polarization in 𝜀𝑟2 material
(g) The angle 𝛼2 between 𝐸⃗2 and normal to surface.
2. A circular line charge of density 𝜌𝑜 C/m of radius ‘a’ is lying in XY plane
with its centre at origin. Calculate the potential at point (0,0,h).
3. Three point charges 3C, 4C and 5C are situated in free space at three
corners of an equilateral triangle with side 5cm. Find the energy density
due to electric field in the triangle.
4. A dielectric sphere of radius ‘b’ and permittivity ‘𝜀’ is situated in vaccum.
It is charged throughout its volume by a charge density 𝜌𝑣 = 5 𝑏⁄𝑟 , ‘r’
being the distance from the centre of sphere. Determine the
electrostatic energy of the system.
Compiled by: Parul Dawar, Inderpreet Kaur, Gunjeet Kaur
GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY
5. For the configuration of figure, find V and E for 𝜃 < 𝜑 < 𝛼 using
Laplace’s equation. Hence find the capacitance of the system.
6. Find the potential that give rise to 𝐸⃗ = 2𝑥𝑦 𝑥̂+𝑥 2 𝑦̂-𝑧̂ .
7. Given cylindrical electric fields
Find the potential difference 𝑉𝐴𝐵 for A(1,0,0) and B(4,0,0).
8. Given a field
Calculate 𝑉𝐴𝐵 for A(-5,2,1) and B(6,1,2).
9. Calculate the field due to a line charge considering it a special Gaussian
surface. (keep it along z-axis)
10. A circular disk r<= 2m, in the z =0 plane has a charge density ρs = 10-8
c/ m2. Determine the electric field 𝐸⃗ at (0, ϕ, h) .
11.Calculate the capacitance between concentric metal spheres of radius 𝑟1
and 𝑟2 with charge Q placed at the outer surface of inner shell.
12.State and derive the Pointing Theorem.
13.Explain briefly the term Polarisation.
14.Current density in a certain region is given by
(a) Find the total current crossing the surface z=3, r<6, in 𝑧̂ direction.
(b) Find
𝜕𝜌𝑣
𝜕𝑡
Compiled by: Parul Dawar, Inderpreet Kaur, Gunjeet Kaur
GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY
(c) Calculate the total current crossing the closed surface bounded by z=0,
z=3, r=1, r=6.
(d) Is
?
15.A current of 25A passes down z-axis, enters a thin shell of radius 6cm
and 𝜃 =
𝜋
2
enters a plane sheet as in figure. Write expressions for the
current densities in spherical shell and in plane.
16.The potential field at any point in a space containing a dielectric material
of relative permittivity 2.1 is given by
Where x,y,z are in meters. Calculate the volume charge density at point
P(2,5,3).
17.A charge distribution with spherical symmetry has volume charge
density
Calculate:
(a) The electric field intensity at all the points
(b) Potential at all the points
(c) Total energy stored in electrostatic field.
18.Given a current density
Compiled by: Parul Dawar, Inderpreet Kaur, Gunjeet Kaur
GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY
𝜋
in spherical coordinates. Find the current crossing the conical strip, 𝜃 = ,
4
0.001≤r≤0.080m.
19.Find the potential and electric field intensity for region between two
concentric right circular cylinders, where v=0 at 𝑟𝑎 =1mm and V=100V at
𝑟𝑏 =20mm. Neglect the fringing.
20.A point charge 𝑄1 =300𝜇𝐶 located at (1,-1,-3)m experiences a force
due to a point charge 𝑄2 at (3,-3,-2)m. Determine 𝑄2 .
Compiled by: Parul Dawar, Inderpreet Kaur, Gunjeet Kaur