1. A negatively charged ebonite rod
attracts a suspended ball of straw. Can we infer that the ball is positively
charged? [No]
2. Can two similarly charged balls
attract each other? [Yes]
3. How can you charged a metal sphere
negatively without touching it? [Induction]
4. If two objects repel one another, you
know both carry either a positive charge or negative charge. How would you
determine whether these charges are positive or negative? [Repulsion Test]
5. Does motion of the body affect its
charge? [No]
6. What is the dimensional formula for $ \epsilon_0 $? [$M^{-1}L^{-3}T^3A^2$]
7. Two small balls having equal positive
charge q coulomb are suspended by two insulating string of equal length l meter
from a hook fixed to a stand. The whole setup is taken in a satellite into
space where there is no gravity. What is the angle between the two strings and
the tension in each string? [$180^0$]
8. Two point charges of + 2μ C and + 6 μ
C repel each other with a force of 12 N. If each is given an additional charge of -4μ C, what will be the new force? [$-4N$]
9. Two point charges of 10-8‑C
and -10-8 C are placed 0.1 m apart. Calculate electric field
intensity at A, B, and C shown in figure. [$E_A = 7.2 \times 10^4 N/C $ along AQ, $E_B = 3.2 \times 10^4 N/C $ along PB, $E_C =9 \times 10^3 N/C $ parallel to PQ]
10. When does a charged circular loop
behave at a point charge? [When the point is very very far away ]
11. How does a free electron at rest move in an electric field? [Opposite to Electric Field]
12. What does (q1 + q 2)
= 0 signify? [Dipole]
13. Two-point charges of +16 μ C and -9 μ C
are placed 8 cm apart in the air. Determine the position of the point at which the
resultant electric field is zero. [24 cm to the right of -9$\mu C$]
14. Four particles, each having a charge q
are placed on the four corners A, B, C, D of a regular pentagon ABCD. The
distance of each corner from the center is a. Find the electric field at the
center of the pentagon. [$\frac{q}{4\pi \epsilon_0 a^2}$ along OE]
15. Two charges of -4 μ C and + 4 μ C are
placed at the points A (1, 0, 4) and B (2, -1, 5) located in an electric field
E = 0.20 $\hat{i}$ V/cm. Calculate the torque acting on the dipole. [$1.131 \times 10^{-4} N-m $]
16. Can we produce high voltage on the
human body without getting a shock? [Yes]
17. Do electron tend to go to region of
high potential or low potential? [High Potential]
18. In a certain 0.1 m3 of
space, electric potential is found to be 5 V throughout. What is the electric
field in this region? [$E = 0$]
19. Write an expression for potential the energy of two charges q1 and
q2 at r1 and r2 in a uniform electric field E. [$P.E. = q_1V(\vec{r_1})+q_2V(\vec{r_2})+ \frac{q_1q_2}{4\pi \epsilon_0 |\vec{r_1}-\vec{r_2}|}$]
20. Two point charges 4 μ C and -2 μ C are
separated by a distance of 1 m in air. Calculate at what point on the line
joining the two charges in the electric potential zero? [$\frac{2}{3}m $ from $4\mu C$ ]
21. An electric field of 20 N/C exists
along the X-axis in space. Calculate the potential difference (VB –
VA) where the coordinates of A and B are given by (i) A (0, 0); B
(4m, 2 m) (ii) A (4 m, 2m); B (6 m, 5 m). [$-80V,-40V$]
22. If the potential in the region of
space around the point (-1 m, 2m, 3m) is given by V = (10 x2 + 5 y2
– 3 z2), calculate the three component of electric field at this
point. [$E_x=20Vm^{-1},E_y=-20Vm^{-1},E_z=18Vm^{-1}$]
23. The electric field in a certain region
of space is $(5\hat{i} + 4\hat{j} -4 \hat{k})$ x 105 N/C. calculate electric flux due to
this field over an area of $ (2\hat{i} – \hat{j})$ x 10-2 m2. [$6 \times 10^3 NC^{-1}m^2$]
24. A point charge q moves from a point P
to the point S along the path PQRS in a uniform electric field E along the positive
direction of the x-axis. Calculate work done in this process, when co-ordinate of
P, Q, R,S are (a, b, 0), (2a 0, 0), (a, -b , 0) and (0, 0, 0) respectively. [$-qEa$]
25. Find the capacitance of the
combination shown in figure between A and B. [$1\mu F$]
26. A network of four 10 μ F capacitors is
connected to a 500 V supply, as shown in figure. Determine the (a)
equivalent capacitance of the network and (b) charge on each capacitor. [$C=13.3\mu F, Q_1=Q_2=Q_3=1.7 \times 10^{-3}C, Q_4=5\times 10^{-3}C$ ]
27. Find equivalent capacity between A
& B, as shown in figure [$1\mu F$]
28. In figure, find equivalent
capacity between A and B. [$5\mu F$]
29. A slab of material of dielectric
constant K has the same area as the plates of a parallel plate capacitor but
has a thickness (3/4)d, where d is the separation of the plates. How is the
capacitance changed when the slab is interested between the plates. [$C=\frac{4K}{3+K}C_0$]
30. Two spheres of radii R and 2 R are
charged so that both of these have the same surface charge density. The spheres are located away from each other and are connected by
a thin conducting wire. Find the new charge density on the two spheres. [$\sigma_1' = \frac{5}{3}\sigma,\sigma_2' = \frac{5}{6}\sigma$]
31. A spherical shell of radius b with
charge Q is expended to radius a. Find the work done by the electric force in
the process? [$W = \frac{Q^2}{8\pi \epsilon_0}[\frac{1}{a}-\frac{1}{b}]$]
32. Sketch a graph to show how charge Q is
given a capacitor of capacity C varies with the potential difference V. [ Figure ]
33. The space between the plate of a
parallel plate capacitor is filled consecutively with two dielectric layers of
thickness d1 and d2 having relative permittivities $\epsilon_1$ and $\epsilon_2$ respectively. If a is area
of each plate, what is the capacity of a capacitor? [$C = \frac{\epsilon_0 A}{\frac{d_1}{\epsilon_1}+\frac{d_2}{\epsilon_2}}$]
34. The equivalent capacitance of the
combination between A and B in the given figure is 4 μ F. pageno.1/160 (i) Calculate the capacitance of capacitor C. (ii) Calculate charge on each capacitor if 12 V battery is connected between A and B. (iii) Calculater potential drop across each capacitor. [$5\mu F, 48\mu C, 2.4V,9.6V$]
35. Calculate the capacitance of the
capacitor C in the figure. The equivalent capacitance of the combination
between P and Q is 30 μ F. [$60\mu F$]
36. A combination of four identical
capacitors is shown in figure . If resultant capacitance of the
combination between the point A and D is 1 μ F. Calculate capacitance of each
capacitor. [$4 \mu F$]
37. A parallel plate capacitor is filled
with a dielectric as shown in figure. What is its capacitance? [$\frac{2\epsilon_0 AK_1K_2}{d(K_1+K_2)}$]
38. Three capacitors of capacitances 2 μ
F, 3 μ F and 6 μ F are connected in series with a 12 V battery. All the
connecting wires are disconnected. The three positive plates are connected
together and the three negative plates are connected together. Find the charges
on the three capacitors after the reconnection. [$\frac{72}{11}\mu C,\frac{108}{11}\mu C,\frac{216}{11}\mu C$]
38. Calculate the charges which will flow
in sections 1 and 2 in figure, when key K is pressed. [$EC_1,\frac{EC_1C_2}{(C_1+C_2)}$]
39. In the circuit shown in figure, the emf of each battery is E = 12 volt and the capacitance are C1
= 2.0 μ F and C2 = 3.0 μ F. Find the charges which flow along the
paths 1, 2, 3 when key K is pressed. [$24\mu C,-36\mu C,12\mu C$]
40. Calculate the equivalent capacitance
between the point A and B in the combination shown in figure [$13.44 \mu C$]
41. If C1 = 3 pF and C2
= 2 Pf, calculate the equivalent capacitance of the network shown in figure between points A and B. [$1pF$]
42. Find the equivalent capacitance of the
combination of capacitors between the points A and B as shown in figure. Also, calculate the total charge that flows in the circuit, when a 100 V battery
is connected between the points A and B. [$C = 20\mu F, Q=2\times 10^{-3}C$]
43. A capacitor is made of a flat plate of
area A and a second plate having a stair-like structure as shown in figure The width of each stair is a and the height is b. Find the capacitance
of the assembly. [$C = \frac{\epsilon_0 A(3d^2+6bd+2b^2)}{3d(b+d)(d+2b)}$]
44. Find out the potential difference
across the plates of 1 μ F capacitor in figure. [$3.82 V$]
45. Find the capacitance of three parallel
plates, each of area A m2 and separated by d1 and d2
meter. The in-between spaces are filled with dielectrics of relative
permittivity $\epsilon_1$ and $\epsilon_2$. The permittivity of free space in $\epsilon_0$. [$C = \frac{\epsilon_1 \epsilon_2 \epsilon_0 A}{\epsilon_1d_2 + \epsilon_2 d_1}$]
46. An uncharged capacitor is connected to
a battery. Show that half the energy supplied by the battery is lost as heat
while charging the capacitor.
47. Obtain the formula for the electric
field due to a long thin wire of uniform linear charge density λ without using
Gauss’s law. [$E = \frac{\lambda}{2\pi \epsilon_0 r}$]
48. A particle of mass m and charge (-q) enters the region between the
two charged plates initially moving along x-axis with speed vx, the
length of plate is l and a uniform electric field E is maintained between the
plates. Show that the vertical deflection of the particle at the far edge of
the plate is \[\frac{qEL^2}{(2 m v_x^2)}\].Compare this
motion with the motion of a projectile in a gravitational field.
49. A spherical conducting shell of inner
radius r1 and outer radius r2 has a charge Q. (a) A charge q is
placed at the center of the shell. What is the surface charge density on the
inner and outer surfaces of the shell? (b) Is the electric
field intensity inside a cavity (with no charge) zero, even if the shell is not
spherical, but has any irregular shape? Explain.[(i) $\sigma_1 = -\frac{q}{4\pi r_1^2},\sigma_2 = \frac{Q+q}{4\pi r_2^2}$, (ii) $Yes$]
50. Two charges q and -3q are placed
fixed on x-axis separated by distance ‘d’. Where should a third charge 2q be
placed such that it will not experience any force? [$x = \frac{(1+\sqrt{3})d}{2}$ from 2q]
51. In 1959, Lyttleton and Bondi suggested
that the expansion of the universe could be explained if matter carried a net
charge. Suppose that the universe is made up of hydrogen atoms with a number
density N, which is maintained a constant. Let the charge on the proton be: ep
= -(1 +y) e where e is the electronic charge. (a) Find the critical
value of y such that expansion may start. (b) Show that the
velocity of expansion is proportional to the distance from the centre. [(a) $\approx 10^{-18}$]
52. Consider a sphere of radius R with
charge density distributed as $ \rho (r) = kr $ for r< R, =0 for r> R. (a) Find the electric
field at all points r. (b) Suppose the total
charge on the sphere is 2e, where e is the electron charge. Where can two
proton be embedded such that the force on each of them is zero. Assume that the
introduction of the proton does not alter the negative charge distribution. [(a) For r<R, $E = \frac{kr^2}{4\epsilon_0}$, For r>R, $E = \frac{kR^4}{4\epsilon_0 r^2}$ (b) $r = \frac{R}{8^{1/4}}$ from center of sphere]
53. Two fixed, identical conducting plates
($ \alpha $ and $\beta $), each of surface area S are charged to -Q and q, respectively, where Q
> q > 0. A third identical plate $ \gamma $, free to move is located on the other side of the plate with charge q at a distance d as shown in figure. Third plate is released and collides with the plate $\beta $. Assume the collision is elastic and the
time of collision is sufficient to redistributed charge amongst $\beta $ and $\gamma $. (a) Find the electric
field acting on the plate $\gamma $ before collision. (b) Find the charges
on $\gamma $ and $\beta $ after the collision. (c) Find the velocity
of the plates $\gamma $ after the collision and at a distance d from the plate $\beta $. [(a) $E = \frac{q-Q}{2\epsilon_0 S}$, (b) $q_{\beta} = (Q+\frac{q}{2}),q_{\gamma} = \frac{q}{2}$, (c) $(Q-\frac{q}{2})\sqrt{\frac{d}{m\epsilon_0 S}}$]
54. There is another useful system of
units, besides the SI/mks A system, called the cgs (centimeter-gram-second). In
this system, Coloumb’s law is given by \[F = \frac{Qq}{r^2} \hat{r}\]where the distance r is measured in cm (=
10-2m), F in dynes (= 10-5 N ) and the charges in
electrostatic units (es units), where 1 es unit of charge = $ \frac{1}{[3]} $ x 10-9
C. The number [3] actually arises from
the speed of light in vacuum which is now taken to be exactly given by c =
2.99792458 x 108 m/s.An approximate value of c then is c =[3] x 108 m/s. Show that the coulomb law in cgs unit yield 1 esu of charge = 1 (dyne)1/2
cm. Obtain the dimensions
of units of charge in terms of mass M, lengh L and time T. Show that it
is given in terms of fractional powers of M and L. Write 1 esu of charge = xC, where x is a dimenionless
number. Show that this gives \[\frac{1}{4\pi \epsilon_0} = \frac{10^{-9}}{x^2} N.m^2/C^2\]
55. Two charges -q each are fixed separated by distance 2d. A third charge q of mass m placed at the mid-point is displaced slightly by x (x
<< d) perpendicular to the line joining the two fixed charges as shown
in figure. Show that q will perform simple harmonic oscillation of time
period. \[T= [\frac{8\pi^3 \epsilon_0 md^3}{q^2}]^{1/2}\]
56. Total charge -Q is uniformly spread along length of a ring
of radius R. A small test charge +q of mass m is kept at the centre of the ring
and is given a gentle push along the axis of the ring. Show that the
particle executes a simple harmonic oscillation. Obtain its time period. [(b) $T = 2\pi \sqrt{\frac{4\pi \epsilon_0 mR^3}{Qq}}$]
57. Prove that a closed equipotential surface with no charge within
itself must enclose an equipotential volume.
58. Calculate potential energy of a point charge -q placed along the
axis due to a charge +Q uniformly distributed along a ring of radius R. Sketch
P.E. as a function of axial distance z from the centre of the ring. Looking at
graph, can you see what would happen if -q is displaced slightly from the
centre of the ring (along the axis)? [$U = \frac{-qQ}{4\pi \epsilon_0\sqrt{R^2+z^2}}$]
59. Find the equation of the equipotential for an infinite cylinder of
radius r0, carrying charge of linear density $ \lambda $. [$r=r_0e^{-2\pi \epsilon_0[V(r)-V(r_0)]/\lambda}$]
60. Two point charges of magnitude + q and -q are placed at (- d/2, 0,
0) and (d/2, 0, 0), respectively. Find the equation of the equipotential
surface where the potential is zero. [$x=0$]
61. A parallel plate capacitor is filled by a dielectric whose
relative permittivity varies with the applied voltage (u) as $ \epsilon =\alpha U $ where $\alpha $ = 2 V-1.
A similar capacitor with no dielectric is charged to U0 = 78 V. It is then connected to the uncharged capacitor with the
dielectric. Find the final voltage on the capacitors. [$6V$]
62. A capacitor is made of two circular plates of radius R each,
separated by a distance d <<R. The
capacitor is connected to a constant voltage. A thin conducting disc of radius
r << R and thickness t << r is placed at the centre of the bottom
plate. Find the minimum voltage required to lift the disc if the mass of the
disc is m. [$V = \sqrt{\frac{mbd^2}{\pi \epsilon_0 r^2}}$]
63. In a circuit shown in figure, initially K1 is
closed and K2 is open. What are the charges on each capacitor. Then K1 was opened and K2 are closed (order
is important ). What will be the charge on each capacitor now?[ C = 9$\mu $F].
64. Calculate potential on the axis of a disc of radius R due to a
charge Q uniformly distributed on its surface. [$V = \frac{2Q}{4\pi \epsilon_0 R^2}[\sqrt{R^2+z^2}-z]$]
65. Two charges q1 and q2 are placed at (0, 0,
d) and (0, 0, -d) respectively. Find locus of points where the potential a
zero. [$x^2+y^2+z^2+[\frac{(q_1/q_2)^2+1}{(q_1/q_2)^2-1}](2zd)+d^2 = 0$]
66. Two charges -q each are separated by distance 2d. A third charge
+q is kept at mid point O. Find potential energy of +q as a function of small
distance x from O due to -q charges. Sketch P.E. v/s x and convince yourself
that the charge at O is in an unstable equilibrium.
67. Two point masses, m each carrying charge -q and +q are attached to
the ends of a massless rigid non conducting rod of length l. The arrangement is
placed in a uniform electric field E such that a rod makes a small angle = 50 with the field direction.
Show that the minimum time needed by the rod to align itself along the field (after it is
set free)is \[T =\frac{\pi}{2}\sqrt{\frac{ml}{2qE}}\]
68. Plate A of a parallel plate air filled capacitor is connected to a
spring having force constant k and plate B is fixed. They are held on a
frictionless tabletop as shown in figure. If a charge +q is placed on
plate A and a charge -q on plate B, how much does the spring expand? [$\frac{q^2}{2\epsilon_0 Ak}$]
69. Find the capacitance of the infinite ladder between points X and
Y, as shown in figure [$2\mu F$]
70. Two identical charged sphere are
suspended in air by strings of equal length and make an angle of 300
with each other. When suspended in a liquid of density 0.8 g/cc., the angle
remain the same. What is the dielectric constant of the liquid? Take density
of the material of the sphere = 1.6 g/c.c. [$K=2$]
71. A thin fixed ring of radius 1 m has a
positive charge of 10-5 C uniformly distributed over it. A particle
of mass 0.9 gram and having a negative charge of 10-6 C is placed on
the axis at a distance of 1 cm from the centre of the ring. Show that the
motion of the negatively charged particle is approximately SHM. Calculate the
time period of oscillation. [$T=0.628 s$]
72. Find the potential difference between
the left and right plate of each capacitor in the circuit shown in figure. [$V_1 = \frac{(E_2-E_1)C_2}{C_1+C_2},V_2 = \frac{(E_2-E_1)C_1}{C_1+C_2}$]
