CHAPTER1: ELECTRIC FIELDS AND GAUSS’ LAW
MULTIPLE CHOICE QUESTIONS
1. The electric flux through
q
surface 1
q
surface 2
q
surface 3
(a) surface 3 is largest
(b) surface 1 is least
(d) same through all surfaces
q
surface 4
(c) same through surface 1 & 2 but less than surface 4
3. A point charge +q, is placed at a distance ‘d’ from an isolated conducted plane. The field at appoint P on
the other side of the plane is
(a) directed perpendicular away from the plane
(b) directed perpendicular towards from the plane
(c) directed radially away from the plane
(d) directed radially towards from the plane
E . d ⃗S =0 over a surface, then
4. If ∮ ⃗
(a) the electric field inside and on it is zero
(b) the electric field inside the surface is necessarily uniform
(c) the number of flux lines entering the surface must be equal to the number of flux lines leaving it
(d) all charges must necessarily be outside the surface
Q
r be the charge density distribution for a solid sphere of radius R and total charge Q for a
4
πR
point ‘P’ inside the sphere at distance r 1 from the centre of the sphere, the magnitude of electric field is
2
2
Q
Q r1
Q r1
(a) zero
(b)
(c)
(d)
2
4
4
4 π ϵ 0 r1
4 π R ϵ0
3 π R ϵ0
5. Let ρ ( r )=
6. The system for which electric field at distances 1cm, 2cm and 3cm are in the ratio 1: 1/8: 1/27 is
(i) point charge
(ii) charged sphere
(iii) linear charged conductor
(iv) electric dipole.
7. An electric dipole is placed at an angle of 60◦ to a non-uniform electric field. The dipole will experience
(a) a torque as well as translational force.
(b) a torque only
(c) a translational force only in the direction of the field.
(d) a translational force only in a direction normal to the field.
8. Figure shows electric field lines in which an electric dipole ‘p’ is placed as shown. Which of the
following statement is correct?
(a) the dipole will not experience any force
(b) the dipole will experience a force towards right
(c) the dipole will experience a force towards left, because the field strength is more at –q.
(d) the dipole will experience a force upwards
-q
p
+q
Reason –assertion:
In each of the following questions, a statement of Assertion (A) is given followed by a corresponding
of reason (R) just below it. Of the statements, mark the correct answer as:
(a) If both assertion and reason are true and reason is the correct explanation of assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of assertion.
(c ) If assertion is true but reason is false.
(d) If both assertion and reason are false.
12. Assertion: The charge given to a metallic sphere does not depend on whether it is hollow or solid.
Reason: Since the charge resides only on the surface of the conductor. (a)
13. Assertion: Charge is quantized because only integral number of electrons can be transferred.
Reason: There is no possibility of transfer of some fraction of electron. (a)
14. Assertion: Electric filed lines start at positive charges and end at negative charges.
Reason: Filed lines are continuous curves without any breaks and they form closed loop. (c)
15. Assertion: Total flux through a closed surface is zero if no charge is enclosed by the surface.
Reason: Gauss law is true for any closed surface, irrespective of its shape or size. (a)
COLOUMB’S LAW
1.
Ans.
A glass rod rubbed with silk acquired a charge + 1.6x10-14c. What is the charge on the silk?
- 1.6x10-14 C
2.
F=
State Coulombs Law. Write its Vector form.(Ans. ⃗
1 q1q2 ^
r)
4 π ε0 r2
3.
In a hydrogen atom, an electron revolves around a proton. Which of these two exerts a greater
electrostatic force on the other?(Ans: Both will be same)
4.
Define dielectric constant of a medium. Dielectric constant of a medium is unity. What will be its
permittivity?(Ans: The ratio of the permittivity of the substance to the permittivity of the free space.
ε
ε r=
e0
5.
Force between two point charges kept at a distance γ apart in air is F. If these charges are kept in the
water at the same distance how does the force between them change?
1
Ans: As the force varies with the permittivity as F α , it will reduce 80 times.
εr
6.
Two electrically charged particles, having charges of equal magnitude, when placed at a distance
‚d‘ from each-other, experience a force of attraction F. These two particles are put in contact and again
placed at the same distance from each-other. What is the nature of the force between them now?
Ans: Yes. Due to redistribution of charges both sphere will acquire same amount of charge with same
sign. Thus it will be repulsive. The magnitude of force will reduece.(additivity of charges)
7.
A thin metallic spherical shell of radius R carries a charge Q on its surface. A point charge Q/2
is placed at its centre C and another charge +2Q is placed outside the shell at a distance x from the centre as
shown in the figure. Find (i) the force on the charge at the centre of shell and at the point A, (ii) the electric
flux through the shell.
ELECTRIC FIELD DUE TO CHARGE SYSTEMS & ELECTRIC DIPOLES
1.
Give two properties of electric lines of force.
Ans: 1. They always start from positive charge and end on the negative charge. Hence, they are open
curves.
2. They don’t intersect each-other otherwise there will be two directions of electric filed at that
point. This is not possible.
2.
i)
ii)
iii)
Draw electric lines of force due to
an isolated positive point charge (q>o)
an isolated negative point charge (q>o)
a system of negative and positive charges.
3.
Two point electric charges of unknown magnitude and sign are placed a distance “d’ apart. The
electric field intensity is zero at a point, not between the charges but on the line joining them. Write two
essential conditions for this to happen.
Ans: (i) Charges must be of opposite signs only then the direction of electric fields would be opposite
to each-other.
(ii) The charge farther from the point of observation must be of larger magnitude.
4.
An electric dipole, when held at 600 with respect to a uniform electric field of 104N/C, experiences a
torque of 9 x 10-26Nm. Calculate the dipole moment of the dipole.
Ans: p = 10.39×10−30 C-m
5.
An electric dipole is held in a uniform electric field . (i) Show that no translatory force acts on it
(ii) Derive an expression or the torque acting on it .
Hint: (i) Net force on a dipole placed in a uniform electric field is zero.
6.
Two point charges +Q & +4Q are separated by a distance of 6a. Find the point on the lining joining
the two charges where the electric field is zero?
Ans: The point is 2a distance from +q charge.
7.
Two small identical electrical dipoles AB and CD , each of dipole moment ‘p’ are kept at an angle
of 1200 as shown in the figure. What is the resultant dipole moment of this combination? If this system is
subjected to electric field E along +X direction, what will be the magnitude and direction of the torque
acting on this? (Ans: Dipole moment = p, torque = pE/2)
8.
Two point charges 3μC and -3μC are located 20cm apart in vacuum.
(a)
Calculate the electric field at the mid-point of the line joining the two charges.
(b)
What is the force experienced by a negative test charge of magnitude 1.5X10-9 C placed at this
point?
Ans: (a) E = 5.4 x 106 N/C
(b) F = 8.1 x 10-3N
9.
Two long thin parallel wires having linear charge density 4 x 10–9 C/m and – 3x 10–9 C/m are kept 20
cm apart in air. Find the magnitude and direction of the electric field at a point 10 cm from each wire.
Ans: E = 1.8 x 1018 N/C outward
10.
Two extremely small charged copper spheres have their centres separated by a distance of 50cm in
vacuum.
a) What is the mutual force of electrostatic repulsion if the charge on each sphere is 6.5x10 -7 C?
b) What will be the force of repulsion if:
(i) the charge on each sphere is doubled and their separation is halved?
(ii) the two spheres are placed in water? ( di-electric constant of water = 80)
Ans: (a) F = 1.52 x 10-2N
(b) (i) F = 0.243N (ii) F’ = F/80
ELECTRIC FLUX & GAUSS LAW
1.
What is the electric flux through a cube of side 1 cm which encloses an electric dipole ?
2.
If the radius of the Gaussian surface enclosing a charge is halved, how does the electric flux
through the Gaussian surface change?
3.
Two charges of magnitudes -3Q and +2Q are located at points (a,0) and (4a,0) respectively. What is
the electric flux due to these charges through a sphere of radius ‘5a’ with its centre at the origin?
4.
Two charges of magnitudes +4Q and - Q are located at points (a,0) and (-3a,0) respectively. What is
the electric flux due to these charges through a sphere of radius ‘2a’ with its centre at the origin?
5.
Using Gauss’s theorem, show that the interior of a conductor can have no excess charge in static
situation.
6.
Define the term Electric flux. What is its S.I. Unit? An electric flux of -6x10 3 Nm2/c passes
normally through a spherical Gaussian surface of radius 10 cm, due to point charge placed at the centre.
a.
What is the charge enclosed bye the Gaussian surface?
b.
If the radius of the Gaussian surface is doubled, how much flux would pass through the surface.
c.
Plot E versus R and V versus R graphs.
7.
Two concentirc metallic spherical shells of radii R and 3R are given charges Q 1 and Q2 respectively.
The surface charge densities on the outer surfaces of the shells are equal. Determine the ratio Q 1:Q2.
8.
Use Gauss’s law to find the electric field due to a uniformly charged infinite plane sheet. What is
the direction of field for positive and negative charge densities?
9.
A charge is distributed uniformly over a ring of radius ‘a’. Obtain an expression for the electric
intensity E at a point on the axis of the ring. Hence show that for points at large distances from the ring, it
behaves like a point charge.
10.
S and S are two hollow concentric spheres enclosing 2Q and 4Q respectively as shown in the
figure.
1
2
(i) What is the ratio of the electric flux through S1 and S2?
(ii) How will the electric flux through the sphere S1 change, if a medium of di-electric constant €r is
introduced in the space inside S1 in place of air?
11.
A hollow cylindrical box of length 1m and area of cross-section 25cm2 is placed in a three
dimensional co-ordinate system as shown in the figure. The electric field in the region is given by E=50xi,
where E is in NC-1 and x is in metres. Find
(i) Net flux through the cylinder
(ii) Charge enclosed by the cylinder.
OR
A uniform electric field E=Exi N/C for x>0 and E=-Exi N/C for x<0 are given. A right circular cylinder of
length l cm and radius r cm has centre its centre at the origin and its axis along the x-axis. Find out the net
outward flux. Using Gauss’s law write the expression for the net charge within the cylinder.
12. On the basis of Gauss’ theorem prove that, for a point outside a charged spherical shell, it behaves as a
point charge.
13. A small metal sphere carrying charge +Q is located at the centre of a spherical cavity in a large
uncharged metal sphere as shown in the figure. Use Gauss’s theorem to find the electric field at points P 1
and P2.
14. (i) “Gauss‘ law in electronics is true for any closed surface, no matter its shape or size is.” Justify this
statement with the help of a suitable example.
(ii) Use Gauss’s law to prove that the electric field inside a uniformly charged spherical shell is zero.