Download Revision Problems in Electrostatics.

REVISION PROBLEMS IN ELECTROSTATICS
Q. 1. Find out points along the line joining two charges + q and –3q where (i) V = 0, (ii) E = 0.
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Q. 2. Two identical parallel plate capacitors C1 and C2 have equal potential C each. The plates
are now filled with dielectrics as shown. If the two capacitors still have equal capacitance,
calculate K. (Given: K1 = 3 and K2 = 2,)
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Q. 3. Three charges of 12 mC; 16 mC and 6 mC are placed at points (0, 0); (4, 0) and (0, 3) as shown in
figure. Calculate the work done to move 6 mC charge from B(0, 3) to C(0, 2). (All distances are in metres)
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Q. 4. A charged spherical drop of radius R has a potential of 100 V on its surface. The drop is sprayed
into 1000 smaller identically charged drops. What will be potential on surface of each of these tiny
drops?
(Given that capacitance of a sphere of radius x equals 4π ∈0 x).
Q. 5. Mr. Ram travelling in a car during a heavy thunderstorm spots a man standing under a
tree. He asks the man to come inside the car to save him from a probable natural calamity.
(a) Why did Mr. Ram consider the man to be in danger?
(b) Why Mr. Ram thought that he and the man could escape the natural calamity inside
the car?
(c) List two qualities exhibited by Mr. Ram.
Ans. (a) The man could be electrocuted due to lightning.
(b) Inside the car, a hollow conductor, electric field is zero.
(c) (i) Scientific temperament
(ii) Helpful nature
(iii) Value for life
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Q. 6
(i) the electric flux through the cube.
(ii) the net charge inside the cube.
Q. 7.
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Ans.
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Q. 8. Obtain an expression for the capacitance of a parallel plate capacitor. How will the capacitance
vary if the distance between the plates is reduced by 20%?
A combination of four capacitors C1; C2; C3 and C4 is as shown below. A potential difference
of 10V is applied between A and B.
Calculate the
(i)
ratio of energy stored in the four capacitors (ii) charge stored in each of the capacitors.
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Ans.
∴ The capacitance increases by 0.25 C or 25%.
Q. 9. Why is it necessary that the field lines from a point charge placed in the vicinity of a
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conductor must be normal to the surface of the conductor at every point?
Ans. As otherwise; the electric field will have a component parallel to the conductor making
free electrons drift till this component becomes zero.
Q. 10. Figure shows a sheet of aluminium foil of negligible thickness placed
between the plates of a capacitor. How will its capacitance be affected if:
(i) the foil is electrically insulated?
(ii) the foil is connected to the upper plate with a conducting wire?
Ans. (i) Capacitance of a parallel plate capacitor with a conducting slab of thickness ‘t’
between the plates is given by
Q. 11. Three points A, B and C are in a uniform electric field (E) of 9.5 × 103 NC–1 as shown
in the figure. Find the potential difference between A and C.
Ans.
Q. 12. The sum of two point charges is 7 µC. They repel each other with a force of 1 N
when kept 30 cm apart in free space. Calculate the value of each charge.
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Q. 13. Define the term ‘electric dipole moment.’ Is it scalar or vector? Deduce an
expression for the electric field at a point on the equatorial plane of an electric
dipole of length 2a.
Ans. The electric dipole moment of a dipole is defined as the product of either of the
charges and the distance between them.
It is a vector directed from Negative to Positive charge.
Electric field intensity at a point on equitorial line of an electric dipole
Consider a point P at a distance ‘r’ from the mid-point ‘O’ on the equitorial line of an electric
dipole (± q, 2a) as shown.
Electric field intensity at P due to charge at A.
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Q. 14. Find the amount of work done in rotating an electric dipole, of dipole moment 3 × 10–8 Cm,
from its position of stable equilibrium, to the position of unstable equilibrium in a uniform electric
field of intensity 104 N/C.
Q. 15. Justify that the electrostatic potential is constant throughout the volume of a charged
conductor and has the same value on its surface as inside it.
Ans. The electric field intensity within a conductor is zero and has no tangential component on the
surface of the conductor. Hence a small test charge placed inside the conductor experiences no force.
The test charge can be moved between any two points inside the conductor without doing any work.
Similarly the work done to move a test charge from inside the conductor to a point just on its surface is
zero.
The work done to move the charge from one point to the other on the surface of the conductor is also
zero. Hence the entire volume of the conductor and its surface is equipotential i.e. has the same value of
potential.
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Q. 16. Given V = x2y + yz.
Calculate (i) X-component of electric field at point (1, 3, 1). (ii) Magnitude of E at (1, 3, 1).
Q. 17. A parallel plate capacitor of plate separation ‘d’ is charged to a potential difference ΔV. A
dielectric slab of thickness ‘d’ and dielectric constant ‘k’ is introduced between the plates while the
battery remains connected to the plates.
(i) Find the ratio of energy stored in the capacitor after and before the dielectric is introduced. Give the
physical explanation for this change in stored energy.
(ii) What happens to the charge on the capacitor?
Ans. (i)
(ii)
Charge on the capacitor before introducing slab = Q = C (ΔV)
Charge after introducing the slab = C′ (ΔV) = KC (ΔV)
Hence the charge also becomes K times the original charge.
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