CHAPTERWISE PRACTICE PAPER : ELECTROSTATICS
ORGENERAL INSTRUCTIONS
(i) All questions are compulsory. There are 26 questions in all.
(ii) This question paper has five sections: Section A, Section B, Section C, Section D and Section E.
(iii) Section A contains five questions of one mark each, Section B contains five questions of two marks each, Section C contains twelve questions of three marks each, Section D contains one value based question of four marks and Section E contains three questions of five marks each.
(iv) There is no overall choice. However, an internal choice has been provided in one question of two marks, one question of three marks and all the three questions of five marks weightage. You have to attempt only one of the choices in such questions.
Time Allowed : 3 hours Maximum Marks : 70
physics for you|june ‘15
52
A capacitor of capacitance C1 is charged to a potential V. On disconnecting with the battery, it is connected with an uncharged capacitor of capacitance C2. Find the ratio of total electrostatic potential energy before and after.
10. An electron is constrained to move along the axis of the ring of charge q and radius a. Show that the electron can perform oscillations whose frequency is given by ω
= peqe ma 4 0 3.
section-c
11. Dedue the expression for the capacitance of a parallel plate capacitor when a dielectric slab is inserted between its plates. Assume the slab thickness is less than the plate separation.
12. Two point charges + 4e and + e are fixed at a distance a apart. Where should a third point charge q be placed on the line joining the two charges that it may be in equilibrium? In which case the equilibrium will be stable and in which unstable?
13. A small sphere of radius r and charge q is enclosed by a spherical shell of radius R and charge Q. Show that if q is positive, charge q will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge Q on the shell is.
14. Two charged conducting spheres of radii a and b are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.
15. Derive an expression for the torque on an electric dipole placed in a uniform electric field. Hence define dipole moment.
Two point charges +q and –q are placed distance OR d apart. What are the points at which the resultant electric field is parallel to the line joining the two charges?
16. (a) Determine the electrostatic potential energy of a system consisting of two charges 7 mC and –2 mC (and with no external field) placed at (–9 cm, 0, 0) and (9 cm, 0, 0) respectively.
(b) How much work is required to separate the two charges infinitely away from each other?
(c) Suppose the same system of charges is now placed in an external electric field E = A(1/r2);
A = 9 × 105 N C–1 m2. What would the electrostatic energy of the configuration be?
17. A charged particle, of charge 2 mC and mass 10 milligram, moving with a velocity of 1000 m s–1 enters a uniform electric field of strength 103 N C–1 directed perpendicular to its direction of motion.
Find the velocity and displacement, of the particle after 10 s.
18. A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?
19. A spherical capacitor has an inner sphere of radius 12 cm and outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5 mC. The space between the concentric spheres is filled with liquid of dielectric constant 32.
(a) Determine the capacitance of the capacitor.
(b) What is the potential of the inner sphere?
(c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explain why the latter is much smaller.
20. Obtain the equivalent capacitor of the network in figure. For a 300 V supply, determine the charge and voltage across each capacitor.
21. Consider three charges q1, q2, q3 each equal to q at the vertices of an equilateral triangle of side l. What is the force on a charge Q (with the same sign as q) placed at the centroid of the triangle?
22. Obtain the formula for the electric field due to a long thin wire of uniform linear charge density l without using Gauss’s law.
section-d
23. Father of Devansh is a surgeon and has a video monitor, Devansh observed that after the use the video monitor surface remain charged for long. He further heard his father instructing his assistant not to bring his finger close to the screen or touch the screen with contaminated gloves as the screen may become a source of bacteria. Devansh asked for the explanation from his father and shared his learning with his classmates during the physics period. His teacher and classmates had appreciations for him.
(i) What values had Devansh shown?
(ii) How did the father explain his observations?
physics for you |june ‘15 53 section-e
24. Define dipole moment of an electric dipole. Show mathematically that the electric field intensity due to a short dipole at a distance d along its axis is twice the intensity at the same distance along the equatorial axis.
What is an electric dipole? An electric dipole is OR placed in a uniform electric field at some angle q.
Deduce the expression for its potential energy.
What is physical significance of electric dipole?
25. Draw a labelled diagram of Van de Graaff generator.
State its working principle to show how by introducing a small charged sphere into a larger sphere, a large amount of charge can be transferred to the outer sphere. State the use of this machine and also point out its limitations.
State Gauss’s theorem in electrostatics and express OR it mathematically. Using it, derive an expression for electric field at a point near a thin infinite plane sheet of electric charge. How does this electric field change for a uniformly thick sheet of charge?
26. Derive an expression for the energy density in a parallel plate capacitor.
A parallel plate capacitor with air as dielectric is charged by a dc source to a potential V. Without disconnecting the capacitor from the source, air is replaced by another dielectric medium of dielectric constant 10. State with reason, how does (i) electric field between the plates and (ii) energy stored in the capacitor change?
What are conductors? Explain the electrostatics of OR conductors.
solutions
1. The electric field due to an electric dipole exhibits cylindrical symmetry with axis as the axis of cylinder.
2. Yes, it is possible to move a charge in an electric field without doing any net work. If electric potential of initial and final points is same,
i.e., VA = VB, then WAB = q(VB – VA) = 0
3. The curve 1 represents variation of electric field E with distance r normal to a long uniformly charged straight wire because here E ∝ 1/r and slope of curve 1 is the least. The curve 3 represents E – r curve for an electric dipole because here E ∝ 1/r3 and slope of curve 3 is maximum.
Then, the curve 2 should represent E–r graph for a point charge, because here E ∝ 1/r2. not possible to store a charge of 1 C in a spherical conductor of radius 1 m.
5. As, electric force between two point charges q1 and q2 in a medium = electric force between same charges in free space
k q q
Then, potential at the surface of each drop,
V q
=4pe 0r
and surface density of charge, σ= qp
r 4 2
When n drops coalesce to form a single bigger drop of radius R, total volume remains unchanged.
Hence, 4
3 4
3 3 3
pR = ×n pr
⇒ R = (n)1/3r
and total charge on the bigger drop, Q = nq
\ Potential of bigger drop,
′ = = =
and new surface charge density,
′ = = =
and electric potential at the centre O2 of 2nd ring,
V q
physics for you|june ‘15
8. The arrangement shown in the figure is equivalent to two capacitors each having a plate area A/2 and plate separation d. The two capacitors are filled with dielectrics of dielectric constants K1 and K2 respectively and are joined in parallel.
\ C =K A =
\ Net capacitance of the capacitors,
C C C A
d K K
= 1+ 2=e20 ( 1+ 2)
9. We know that potential energy of an electric dipole is given by
On the basis of this data, we plot the curve as shown in the given figure. It is a part of cosine curve.
OR