Coulomb’s Law
Objective Question
Q.1 When a glass rod
is rubbed with silk, it acquires a positive charge because:
(a) protons are added to it (b) electrons
are added to it
(c) electrons are removed to it (d) protons are removed from it.
Q.2 The number of
electrons contained in 1 coulomb of charge equals :
(a) 6.25 ´ 1017 (b) 6.25
´ 1018 (c) 6.25 ´ 1019 (d) 1.6 ´ 1019
Q.3 Two charges +1 mC and + 5 mC are placed a
distance apart. The ratio of the forces acting on them are :
(a) 1 : 5 (b) 5
: 1
(c) 1
:1
(d) 1 : 25
Q.4 The ratio of the
forces between two tiny bodies with constant charges in air and an insulating
medium of dielectric constant K is :
(a) 1 : K (b) K
: 1
(c) 1
: K2 (d) K2
: 1
Q.5 The dielectric
constant K of an insulater can be :
(a) -1 (b) 0 (c) 0.5 (d) 5.
Q.6 The SI unit of free-space permittivity e0 is :
(a) Nm2C-2 (b) Nm-2C2 (c) N-1m-2C2 (d) N-1m2C2.
Q.7 The ratio of the gravitational and the
electrostatic forces between two electrons at some distance apart is :
(a) 1043 (b) 1039 (c) 10-39 (d) 10-43.
Q.8 Three charges 4q, Q and q are in a
straight line in the position 0, l/2 and re and l respectively.
Resultant force at q will be zero if Q is equal to :
(a) -q (b) -2q (c) -q/2 (d) 4q.
Q.9 A charge q is
placed at the center of the line joining two equal charges Q. The system of the
three charges will be in equilibrium if q is equal to :
(a) -Q/2 (b) -Q/4 (c) +Q/4 (d) Q/2.
Q.10 Two point charges + 4mC and + 2mC repel
each-other with a force of 8N. If a charge of -4mC is added to each of these charges, the force would be
(a) zero (b) 8N (c) 4N (d) 12N
Q.11 Two point charges certain distance apart
in air repel each other with a force F. A glass plate is introduced between the
charges. The force becomes F`, where
(a) F` < F (b) F`
= F (c) F` > F (d) data is insufficient.
Q.12 Force between two charges separated by a
certain distance in air is F. If each charge were doubled and distance between
them also doubled, force would be
(a) F (b) 2F
(c) 4F (d) F/4
Q.13 When a body is charged by induction,
then the body
(a) becomes neutral (b) does
not lose any charge
(c) loses whole of
the charges on it (d) loses
part of the charge on it
Q.14 A polythene
piece, rubbed with wool, is found to have negative charge of 4 ´ 10-7C.
The no. of electrons transferred from wool to polythene are
(a) 1.5 ´ 1012 (b) 2.5
´ 1012 (c) 2.5 ´ 1013 (d) 3.5
´ 1013
Q.15 When a piece of polythene is rubbed with
wool, a charge of –2 ´ 10-7 C
is developed on polythene. What is the amount of mass, which is transferred to
polythene?
(a) 5.69 ´ 10-19
kg (b) 6.25
´ 10-19
kg
(c) 9.63 ´ 10-19
kg (d) 11.38
´ 10-19
kg
Q.16 If a body is positively charged, then it
has
(a) excess of
electrons (b) excess
of protons
(c) deficiency of
electrons (d) deficiency
of neutrons
Q.17 On charging by conduction, mass of a
body may
(a) increase (b) decrease
(c) increase or
decrease (d) none.
Q.18 An uncharged insulted conductor A is
brought near a charged insulted conductor B.
(a)
the charge and potential of B, both remain constant
(b)
both change
(c)
the charge remains constant, but potential decreases
(d)
the charge remains constant but potential increases
Q.19 A given charge is situated at a certain
distance from an electric dipole in the end on position, experiences, a force
F. If the distance of charge is double, the force acting on the charge will be
(a) F (b) F/2 (c) F/4 (d) F/8
Q.20 Point charges
+4q, -q and +4q are kept on the x-axis at points x = 0, x = a and x = 2 a
respectively
(a)
only -q is in stable
equilibrium (b) all the charges are in stable
equilibrium
(b)
all the charges are in unstable equilibrium (d) none of the charges in equilibrium
Q.21 There are two charges +1mC and +5mC.
The ratio of the force the acting on them will be
(a) 1 :
1 (b) 1
: 2 (c) 1 : 3 (d) 1
: 4
Q.22 Coulomb’s law is
true for
(a) atomic distances
(= 10-11 m) (b) nuclear
distance (= 10-15 m)
(c) charged
as well as for uncharged particles (d) all the distances
Q.23 Two charges are placed a certain
distance apart. A metallic sheet is placed between them. What will happen to
the force between the charges?
(a) increase
(b) decrease (c) remain
unchanged (d) either ‘a’ or ‘b’.
Q.24 Two equally
charged identical metal spheres A and B repel each other with a force 3 ´ 10-5
N. Another identical uncharged sphere C is touched to A and then placed at the
mid-point between A and B. Net force on it is
(a) 1 ´ 10-5N (b) 2 ´ 10-5N (c) 1.5 ´ 10-5N (d) 3
´ 10-5N
Q.25 Which of the
following is best insulator ?
(a) Carbon (b) Paper (c) Graphite (d) Ebonite.
Q.26 A cylindrical
conductor is placed near another positively charged conductor. The net charge
acquired by the cylindrical conductor will be
(a) positively only (b) negative
only
(c) zero (d) either
positive or negative.
Q.27 The point
charges of 10mC and –5 mC are separated
in air by 1m. The ratio of force exerted by one on the other is
(a) 1 : 2 (b) 2
: 1 (c) 1
: 1 (d) none
of the above.
Q.28 An attractive force of 5 N is acting
between two charges of + 2mC and - 2mC placed at some
distance. If the charges are mutually touched and placed again at the same
distance, the new force would be
(a) 4N (b) zero (c) 10N (d) 20N
Q.29 Two spheres A
and B of exactly same mass are given equal positive and negative charges
respectively. Their masses after charging
(a) remain unaffected (b) mass
of A > mass of B
(c) mass of A < mass of B (d) nothing
can be said.
Q.30 An ebonite rod
acquires a negative charges of 3.2 ´ 10-10C. The number of excess electrons it has is
(a) 2 ´ 109 (b) 2 ´ 10-9 (c) 2 ´ 10-29 (d) 2 ´ 1029
Answer
Coulomb’s Law
1.
|
(c)
|
2.
|
(b)
|
3.
|
(c)
|
4.
|
(b)
|
5.
|
(d)
|
6.
|
(c)
|
7.
|
(d)
|
8.
|
(a)
|
9.
|
(b)
|
10.
|
(a)
|
11.
|
(a)
|
12.
|
(a)
|
13.
|
(b)
|
14.
|
(b)
|
15.
|
(d)
|
16.
|
(c)
|
17.
|
(c)
|
18.
|
(a)
|
19.
|
(d)
|
20.
|
(d)
|
21.
|
(a)
|
22.
|
(d)
|
23.
|
(b)
|
24.
|
(d)
|
25.
|
(a or all)
|
26.
|
(c)
|
27.
|
(c)
|
28.
|
(b)
|
29.
|
(c)
|
30.
|
(a)
|
Q.1 A table–tennis ball
which has been covered with a conducting paint is suspended by a silk thread so
that it hangs between two metal plates. One plate is earthed. When the other
plate is connected to a high voltage generator, the ball
(a) is
attracted to the high voltage plate and stays there
(b) hangs without moving
(c) swings
backward and forward hitting each plate in turn
(d) is
repelled to the earthed plate and stays there
Q.2 Five balls
numbered 1 to 5 are suspended using separate threads. Pairs (1, 2), (2, 4) and
(4, 1) show electrostatic attraction while pairs (2, 3) and (4, 5) show
repulsion. Then
(a) Ball – 1 is positively charged
(b) Ball – 1 is
negatively charged
(c) Ball – 1 is neutral
(d) Ball – 1 is positively charged and Ball
– 2 is negatively charged
Q.3 The ratio of the
forces between two small spheres with constant charges, in air and in a medium
of dielectric constant K, is
(a) 1 : K (b) K : 1 (c) 1
: K2 (d) K2
: 1
Q.4 A certain charge
Q is divided at first into two parts q and q’. Later on, the charges are placed at certain distance. If the
force of interaction between two charges is maximum, then
(a) q/q’=2 (b) q/q’=1 (c) q/q’=
4 (d) q/q’=3
Q.5 A pendulum bob
of mass 80 mg and carrying a charge of 2´10-8C is at rest in horizontal uniform electric field
of 20,000V/m. The tension in the thread of the pendulum is
(a) 2.2 ´ 10-4N (b) 4.4´10-4N (c) 8.9´10-4N (d) 17.6´10-4N
Q.6 A soap bubble is
given a negative charge. Then its radius
(a) decreases (b) increases
(c) remain
unchanged (d) nothing can be said as sufficient
information is not available
Q.7 A negatively
charged particle is situated on a straight line joining two other stationary
particles each having charge + q. The
direction of motion of negatively charged particle will depend on
(a)
the magnitude of its charge (b) the position where it is situated
(c) both
magnitude of its charge and its position (d)
the magnitude of + q
Q.8 The charge +q are placed at the four corners of a
square. How much charge must be placed at its centre so that the whole system
is in equilibrium?
(a) –q/4
(1+2Ö2) (b) –q/2 (1+2Ö2) (c) –q/8
(1+2Ö2) (d) +q/4 (1-2Ö2)
Q.9 An electron
(mass=9.1´10-31kg)
and charge = 1.6´10-19C
is sent in an electric field of intensity 1´106V/m. How long would it take for the electron,
starting from rest to attain one-tenth velocity of light?
(a) 1.7 ´ 10-12s (b) 1.7 ´ 10-6
s (c) 1.7 ´ 10-8
s (d) 1.7´10-10
s
Q.10 An
electron of mass Me, initially at rest, moves through a certain
distance in a uniform electric field in time t1. A proton of mass Mp
also initially rest, takes time t2 to move through an equal distance
in this uniform electric field. Neglecting the effect of gravity, the ratio t2/t1
is nearly equal to
(a) 1 (b) ÖMp / Me (c) ÖMe / Mp (d) 1836
Q.11 An
electric field can deflect
(a) neutrons (b) X-rays (c) g-rays (d) a-particles
Q.12 The electric field that can
balance a deutron of mass 3.2 ´ 10-27 kg is
(a) 19.6 ´ 10-10 N/C (b) 19.6
´ 10-8 N/C
(c) 19.6 ´ 1010 N/C (d) 19.6
´ 108 N/C
Q.13 Electric lines of forces
(a) exist everywhere
(b) exist only in the immediate vicinity of electric charges
(c) exist only when both positive and negative charges are near one another
(d) are imaginary.
Q.14 The
dimensional formula of electric intensity
(a) MLT-2A-1 (b) MLT-3A-1 (c) ML2T-3A-1 (d) ML2T-3A-2
Q.15 A positive charged ball hangs from a silk thread. We put a positive
test charge q0 at a point and measure F/q0, then it can be
predicted that the electric field strength E will be
(a) = F/q0 (b) > F/q0 (c) < F/q0 (d) none of the
above.
Q.16 A
drop of oil of density r and radius r carries a
charge q when placed in an electric field E, it moves upwards with a velocity n. If r0 is the density of air, h be the viscosity of the air, then which of
the following forces is directed up-wards
(a) qE (b) 6phrn (c) 4/3pr3 (r -r0) (d) none
of the above.
Q.17 A proton and an
electron are located in a uniform electric field. They will experience :
(a) equal forces in same direction
(b) forces equal in
magnitude
(c) equal acceleration in opposite
directions
(d) acceleration equal in
magnitude.
Q.18 A
charge q is placed at the centre of the line joining two equal charges Q. The
system of the three charges will be in equilibrium if q is equal to
(a) –Q/2 (b) –Q/4 (c) +Q/4 (d) +Q/2
Q.19 Two
particles, each of mass m and
carrying charge Q, are separated by some distance. If they are in equilibrium
under mutual gravitational and electrostatic forces then Q/m (in C/kg) is of the order of
(a) 10-5 (b) 10-10 (c) 10-15 (d) 10-20
Q.20 Three point
charges are placed at the corners of an equilateral triangle. Assume that only
electrostatic forces are acting
(a) the system will be in equilibrium if the
charges have the same magnitude but not all have the same sign
(b) the system will be in equilibrium if the
charges have different magnitudes and not all have the same sign
(c) the system will be in equilibrium if the
charges rotate about the centre of the triangle
(d) the system can never be in equilibrium
Q.21 Two identical
pendulums, A and B, are suspended from the same point. The bobs are given
positive charges, with A having more charge than B. They diverge and reach
equilibrium, with A and B making angles q1 and q2 with the vertical respectively.
(a) q1 >q2 (b) q1 < q2
(c) q1 = q2 (d) the tension in A is greater than that in
B
Q.22 In a
rectangular polygon of n sides, each
corner is at a distance r from the
centre. Identical charges of magnitude Q are placed at (n-1) corners. The field at the centre is
(a) kQ/r2 (b) (n-1)kQ/r2
(c) n/n-1 k Q/r2 (d) n-1
/nk Q/r2
Q.23 Two identical
metal balls with charges +2Q and –Q are separated by some distance, and exert a
force F on each other. They are joined by a conducting wire, which is then
removed. The force between them will now be
(a) F (b) F/2 (c) F/4 (d) F/8
Electric Filed
ANSWER
1.
|
(c)
|
2.
|
(c)
|
3.
|
(b)
|
4.
|
(b)
|
5.
|
(c)
|
6.
|
(c)
|
7.
|
(b)
|
8.
|
(a)
|
9.
|
(d)
|
10.
|
(b)
|
11.
|
(d)
|
12.
|
(b)
|
13.
|
(d)
|
14.
|
(b)
|
15.
|
(b)
|
16.
|
(a)
|
17.
|
(b)
|
18.
|
(b)
|
19.
|
(b)
|
20.
|
(d)
|
21.
|
(c)
|
22.
|
(a)
|
23.
|
(d)
|
||
Dipole
Q.1 Electric charges
q, q and –2q are placed at
the corners of an equilateral triangle of side l. The magnitude of electric dipole moment of the system is [CPMT-1994]
(a) q l (b) 2q
l (c) Ö3q l (d) 4q l
(a) 1/r (b) 1/r2 (c) r (d) 1/r3
(a) Positive
(b) Negative (c) Zero (d) None of the above
Q.4 An electric dipole has charges +q and –q
at a separation r. At distant d > > r along the axis of the dipole, the
field is proportional to :
(a) q/d2 (b) qr/d2 (c)
q/d3 (d) qr/d3
Q.5 A given charged situated at a certain distance from an electric dipole
in the end on position experiences a force F. If the distance of the charge is
doubled, the force acting on the charge will be : [MNR-86]
(a) 2F (b) F/2 (c) F/4 (d) F/8
Q.6 In case of a dipole filed
(a) Intensity can be zero (b) Potential can be zero
(c) Both can be zero (d) None can be zero.
Q.7 Two
point charges +q & -q are held fixed at (-d, 0) & (d, 0) respectively
for (x, y) co-ordinate system then [IIT-95]
(a) A force and a torque (b) A
force only
(c) A torque only (d) Neither a
force nor a torque.
Q.17 An electric dipole
of moment p is placed at the origin
along the x-axis. The electric field at a point P whose position vector makes an angle q with the
x-axis, will make an angle given by the following, where tan a = ½ tan q ---
(a) a (b) q (c)
q + a (d) q + 2a
Q.18 An electric dipole
placed with its axis at 30°with a uniform
electrical field experience a torque of magnitude 0.032 Nm. If the dipole were
free to rotate, its potential energy in stable equilibrium would be
(a) 0.064J (b) –0.064J (c) 0 (d)
–0.16J
Q.19 A and B are
two points on the axis and the perpendicular bisector respectively of an
electric dipole. A and B are far away from the dipole and at equal distances
from it. The fields at A and B are EA and EB.
(a) EA =EB (b) EA=2EB
(c) EA=-2EB (d) |EB| =1/2 | EA| and EB is perpendicular to EA
Q.20 In the
previous question, let VA and VB be the potentials at A
and B respectively
(a) VA =VB (b) VA=2VB
(c) VA¹ O, VB= 0 (d) VA= 0, VB= o
Q.21 An electric
dipole is placed at the origin and is directed along the x-axis. At a point P,
far away from the dipole, the electric field is parallel to the y-axis. OP makes an angle q with the x-axis
(a) tan q =Ö3 (b) tan q =Ö2
(c) q = 45o (d) tan q =1/Ö2
Answers
Dipole
1.
|
(c)
|
2.
|
(b)
|
3.
|
(c)
|
4.
|
(d)
|
5.
|
(d)
|
6.
|
(b)
|
7.
|
(b,d)
|
8.
|
(c)
|
9.
|
(b)
|
10.
|
(b)
|
11.
|
(c)
|
12.
|
(d)
|
13.
|
(c)
|
14.
|
(b)
|
15.
|
(c)
|
16.
|
(b)
|
17.
|
(b)
|
18.
|
(b)
|
19.
|
(c)
|
20.
|
(c)
|
21.
|
(acd)
|
Gauss’s
Law
Q.1 A
cylinder of radius R and length l is placed in a uniform electric field E
parallel to the cylinder axis. The total flux for the surface of the cylinder
is given by :
(a) 2pR2E (b) 2pR2/E (c) (pR2 + pR2)/E (d) zero.
Q.2 A charge
is placed at the center of a cube with side L. The electric flux linked with
cubical surface is :
[CPMT 1993]
(a) (Q/6L2e0) (b) (Q/L2e0) (c) (Q/e0) (d) zero.
Q.3 A charge Q is situated at
the center of a cube. The electric flux through one of the faces of the cube is
:
(a) (Q/e0) (b) (Q/2e0) (c) (Q/4e0) (d) (Q/6e0).
Q.4 Total electric flux coming out of a unit positive
charge put in air is:
(a) e0 (b) e0-1 (c) (4pe0)-1 (d) 4pe0.
Q.5 A charge body has an electric flux f associated with it. They body
is now placed inside a metallic container. The electric flux f1 outside the container will
be
(a) f1 = 0 (b) 0
< f1 < f (c) f1 = f (d) f1 > f.
Q.6 In a region space having a uniform electric field E, hemispherical bowl
of radius r is placed. The electric flux f through the bowl is
(a) 2p r E (b) 4p r2 E (c) 2p r2 E (d) p r2 E.
Q.7 Positive electric flux indicates that electric lines
of force are directed
(a) outwards (b) inwards (c) outwards or inwards (d) none
of these.
Q.8 Number of electric lines of force emanating from 1 C
of positive charge in a dielectric medium of constant 10 is
(a) 8.85 ´ 10-12 (b) 9
´ 109 (c) 1/4p ´ 9 ´ 109 (d) 1.13 ´ 1011.
Q.9 A sphere of radius 1m encloses a charge of 5mC. Another charge of -5mC is placed inside the sphere. The net
electric flux would be
(a) double (b) four times
(c) zero (d) none of these.
Q.10 The electric flux over a sphere of radius 1m is f. If radius of the sphere were doubled
without changing the charge enclosed, electric flux would become
(a) 2f (b) f/2 (c) f/4 (d) f.
Q.11 Electric
field intensity at a point due to an infinite sheet of charge having surface
charge density s is E. If sheet were
conducting electric intensity would be
(a) E/2 (b) E (c) 2E (d) 4E.
Q.12 In
a certain region of surface, there exists a uniform electric field of 2 ´ 103 k V/m. A rectangular coil of
dimensions 10 cm ´ 20 cm is placed in x-y
plane. The electric flux through the coil is
(a) zero (b) 30 V-m (c) 40 V-m (d) 50 V-m.
Q.13 Two charged
metallic sphere are joined by a very thin metal wire. If the radius of the
larger sphere is twice that of the smaller one, the electric field near the
larger sphere is
(a)
twice that near the smaller sphere
(b)
half of that near the smaller sphere
(c)
the same as that near the smaller sphere
(d)
one-fourth of that near the smaller sphere
Q.14 A point
charge Q is placed outside a hallow spherical conductor of radius R, at a
distance r ( r>R) from its centre C. the filed at C due the induced charges
on the conductors is
(a) zero (b) k
Q/(r-R)2
(c) k
Q/r2, directed towards Q (d) kQ/r2,
directed away from Q
Q.15 A positive
point charge, which is free to move, is placed inside a hollow conducting
sphere with negative charge, away from its centre. It will
(a) move towards the centre
(b) move towards the nearer wall of the
conductor
(c) remain stationary
(d) oscillate between the centre and the
nearer wall
Q.16 In a region
of space, the electric field is in the x –direction and proportional to x,i.e., E =Eox î. Consider an imaginary cubical
volume of edge a, with its edges
parallel to the axes of coordinates. The charge inside this volume is
(a) zero (b) ℇoEoa3 (c) 1/ℇoEoa3 (d) 1/6 ℇoEoa2
Q.17 A charge Q is placed at the mouth of a
conical flask. The flux of the electric field through the flask is
(a) zero (b) Q/ℇo (c) Q/2ℇo (d) < Q/2ℇo
Q.18 A long string with a charge of l per unit length passes through an imaginary cube of edge a. the maximum flux of the electric
field through the cube will be
(a) la/ℇo (b) Ö2la /ℇo (c) 6la2 /ℇo (d) Ö3 la/ℇo
Q.19 If the
electric field id given by 6i + 3j + 4k, calculate the
electric flux through a surface of area 20 units lying in YZ-plane.
(a) 0 (b) Ö100 (c) 120 (d) 40.
Answer
(Gauss’ Law)
1.
|
(d)
|
2.
|
(c)
|
3.
|
(d)
|
4.
|
(b)
|
5.
|
(c)
|
6.
|
(c)
|
7.
|
(a)
|
8.
|
(d)
|
9.
|
(c)
|
10.
|
(d)
|
11.
|
(c)
|
12.
|
(c)
|
13.
|
(c)
|
14.
|
(c)
|
15.
|
(c)
|
16.
|
(b)
|
17.
|
(c)
|
18.
|
(d)
|
19.
|
(c)
|
||
Electric Potential
Q.1 The ratio of the
forces between two small spheres charged to constant potential in air and in a
medium of dielectric constant K is
(a) 1 : K (b) K
: 1 (c) 1 : K2 (d) K2
: 1
Q.2 An infinite
number of electric charges each equal to +q are placed at x = 1, 2, 3, 4, 8 ……
so on. Find the potential at x = 0.
(a) ¥ (b) 0 (c) q/4pe0 (d) 2q/4pe0
Q.3 In a certain
region an uniform field E = Ex i exists. If a small circle is drawn
with the origin as the centre cutting the axes at A (a, 0), B (0, a), C (-a, 0) and D (0,-a), the potential is maximum at
(a) A (b) B (c)
C (d)
D
Q.4 For equal
charges each of Q coulombs are placed
at the four corners of a square of side a
meters. The work done in removing a charge –Q
coulombs from its centre to infinity is
(a) 0 (b) Ö2/4pe0 Q2/a (c) Ö2/pe0 Q2/a (d) Q2/2pe0a
Q.5 The electric
potential in a region along the x – axis varies with x according to the
relation V (x) = 3 +5x2.
Then
(a) the
p.d. between the points x = 1 and x = -2
is –15 V
(b) the
force on +1mC charge at x =-1m is 10mN
(c) the
work done in carrying +1mC charge from origin to x =1 is 6J
(d) the
field near the origin is uniform, along x-axis
Q.6 A hollow charged
metal sphere has radius R. If the potential
difference between its centre and a point at a distance 3R from the centre is V.
the electric field intensity at distance 3R
from centre, is
(a) V/6R (b) V/4R (c) V/3R (d) V/2R
Q.7 A charge Q is distributed over two concentric
hollow spheres of radii r and R (>r) such that the surface densities are equal. The potential at the
common centre is
(a) 1/4pe0. Q. (R2+r2)/ (R + r) (b) 1/4pe0. Q/ (R+r)
(c) 0 (d)
1/4pe0. Q. (r+ R) (r2+ R2)
Q.8 A hollow metal
sphere of radius 5cm is charged such that the potential on its surface is 10V.
The potential at the centre of the sphere is
(a) 0V
(b) 10V
(c) same
as at point 5cm away from the surface
(d) same
as at point 10cm away from the surface
Q.9 A solid
conducting sphere having a charge Q is surrounded by an uncharged concentric
conducting hollow spherical shell. Let the potential difference between the
surface of the solid sphere and that of the outer surface of the hollow shell
be V. If the shell is now given a charge of -3Q, the new potential difference
between the two surfaces is
(a) V (b)
2V (c)
4V (d)
-2V
Q.10 Two concentric
metallic shells of radii R1 and R2 (>R1)
have charges Q1 and Q2 respectively, the potential at a
distance r, where R1< r 2,
(a) Q1+Q2/r (b) Q1/R1+Q2/R2 (c) Q1/r+Q2/R2 (d) Q1/R2+Q1/R2
Q.11 Two identical
thin rings, each of radius R metres
are coaxially placed at a distance R
metres apart. If Q1
coulomb and Q2 coulomb are
respectively the charges uniformly spreads on the two rings, the work done in
moving a charge q from the centre of
one ring to that of the other is
(a) 0 (b)
1/4pe0 . q(Q1
– Q2) /.R (Ö2 – 1) / Ö2
(c) 1/4pe0 . Ö2q(Q1
+ Q2) / R (d)
1/4pe0 . q(Q1
+ Q2) /R (Ö2+1) / Ö2
Q.12 A half ring of radius R has a charge of l per unit length. The potential at the centre of the half ring is
(a) k l/R (b) k l/pR (c) k lp/R (d) klp
Q.13 Charge Q is given a displacement ŕ
=aî + bĵ in an electric field E = E1î +E2ĵ. The
work done is
(a) Q(E1a+E2b) (b) QÖ(E1a)2+(E2b)2
(c) Q(E1+E2)
Öa2+b2 (d) Q(ÖE21+E22) Öa2+b2
Q.14 Let Vo be the potential at the
origin in an electric field E=Exî +Eyĵ. The potential at
the point (x,y) is
(a) Vo-xEx-yEy (b) Vo+xEx+yEy
(c) xEx+yEy-Vo (d) (Öx2+y2) ÖE2x+E2y-Vo
Q.15 The electric potential V at any point x,y,z (all in
metres) in space is given by V = 4x2 volts. The electric field (in
V/m) at the point (1m, 0, 2m) is
(a) -8 î (b) 8 î (c) -16 (d) 8Ö5
Q.16 A no conducting ring of radius 0.5 m carries
a total charge of 1.11 ´ 10-10C distributed no uniformly on its circumference,
producing an electric field E everywhere
in space. The value of the line integral
∫∫=0∫ = ¥ -E. d∫ (∫ = 0 being the centre of the ring) in
volts is
(a) +2 (b) – 1 (c) –2 (d) 0
Q.17 A charge +q is placed at each of the points x =xo,
x =5xo,….ad infinitum on the x-axis,
and a charge –q is placed at each of the points x =2xo,x =4xo,
x =6x0…ad infinitum. Here, xo is a positive constant. Take the electric potential
at a point due to a charge Q at a distance r from it to be Q/(4pℇor). Then, the potential at the origin due to the above
system of charges is
(a) 0 (b) q / 8pℇoxo 1n 2
(c) ¥ (d) q 1n 2/4p ℇoxo
Q.18 A solid sphere of radius R is charged
uniformly. At what distance from its surface is the electrostatics potential
half of the potential at the centre?
(a) R (b) R/2 (c) R/3 (d) 2R
Q.19 A large solid sphere with uniformly distributed
positive charge has a smooth narrow tunnel through its centre. A small particle
with negative charge, initially at rest far from the sphere, approaches it
along the line of the tunnel, reaches its surface with a speed v, and passes through the tunnel. Its
speed at the centre of the sphere will be ?
(a) 0 (b) v (c) Ö2v (d) Ö1.5v
Q.20 Which of the following is not true for a
region with a uniform electric field?
(a) it can have free charges
(b) it may
have uniformly distributed charged
(c) it mat
contain dipoles (d) none of the above
Q.21 ‘All charge on a conductor must reside only
on its outer surface’. This statement is true
(a) in all cases
(b) for spherical conductors only (both solid and hollow)
(c) for hollow spherical conductors only
(d) for conductors which do not have any
sharp points or corners
Q.22 A spherical
conductor A of radius r is placed concentrically inside a conducting shell B of
radius R (R>r).A charge flowing from A to B will be
(a) Q [ R/R + r ] (b) Q [ r/R +
r] (c) Q (d) zero
Q.23 A spherical
equipotential surface is not possible
(a) for a point charge (b) for a dipole
(c) inside a uniformly charged sphere (d) inside a spherical capacitor
Q.24 In a certain charge distribution, all points
having zero potential can be joined by a circle S. Points inside S have
positive potential, and points outside S have negative potential. A positive
charge, which is free to move, is placed inside S
(a) it will
remain in equilibrium
(b) it cam
move inside S, but it cannot cross S
(c) it must
cross S at some time
(d) it
may move, but will ultimately return to
its starting point
Q.25 If the earth’s surface is treated as a
conducting surface with some charge, what should be the order of magnitude of
the charge per unit area, in C/m2, so that a proton remains
suspended in space near the earth’s surface?
(a) 10-18
(b) 10-12 (c) 10-6 (d) 1
Q.26 A simple pendulum of time period T is
suspended above a large horizontal metal sheet with uniformly distributed
positive charge. If the bob is given some negative charge, its time period of
oscillation will be
(a) > T (b) < T
(c) T (d) proportional to its amplitudes
Q.27 A spring-block system undergoes vertical
oscillation above a large horizontal metal sheet with uniform positive charge.
The time period of the oscillation is T. if the block is given a charge Q, its
time period of oscillation will be
(a) T (b) >T
(c)
(d) >T of
Q is positive and < T if Q is negative
Q.28 A large flat metal surface has a uniform charge
density +s. An electron of mass m and charge e leaves the surface at
point A with speed u, and returns to
it at point B. disregard gravity. The maximum value of AB is
(a) u2mℇo/se (b) u2eℇo/ms (c) u2e/ℇo sm (d) u2se/ℇom
Q.29 Small drops of the same size are charged to
V volt each. If n such drops coalesce to form a single large drop, its potential will be :
(a) Vn (b) V/n (c) Vn1/3 (d) Vn2/3
Q.30. Sixty four
equal charged drops are combined to form a big drop. If the potential on each
drop is 10 volt, then the
potential of the big drop will be
(a) 10 V (b) 40 V (c) 160 V (d) 640 V
ANSWER
Electric Potential
1.
|
(a)
|
2.
|
(d)
|
3.
|
(c)
|
4.
|
(c)
|
5.
|
(a), (b)
|
6.
|
(a)
|
7.
|
(d)
|
8.
|
(b)
|
9.
|
(a)
|
10.
|
(c)
|
11.
|
(b)
|
12.
|
(d)
|
13.
|
(a)
|
14.
|
(b)
|
15.
|
(b)
|
16.
|
(a)
|
17.
|
(b)
|
18.
|
(a)
|
19.
|
(c)
|
20.
|
(c)
|
21.
|
(c)
|
22.
|
(d)
|
23.
|
(c)
|
24
|
(b)
|
25.
|
(b)
|
26.
|
(c)
|
27.
|
(b)
|
28
|
(b)
|
29.
|
(d)
|
30.
|
(c)
|
Capacitor
Q.1 A slab of copper
of thickness d/2 is inserted in
between the plates of a parallel plate capacitor, where d is the separation between the two plates. If the capacity of the
capacitor without copper slab is C
and with copper slab is C’ then C, / C.
is
(a) Ö2 (b) 2 (c) 1 (d) 1/Ö2
Q.2 A parallel plate
capacitor is made by stacking n
equally spaced plates connected alternately. If the capacitance between any two
plates is C. Then the resultant
capacitance is
(a) C (b) nC (c) (n-1)C (d) (n+1)C
Q.3 Eight drops of
mercury of equal radii and possessing equal charges combine to form a big drop.
Then the capacitance of big drop compared to each individual drop is
(a) 8 times (b) 4 times (c) 2 times (d) 32 times
Q.4 A parallel plate
capacitor is charged and then isolated. What is the effect on increasing the
plate separation?
Charge Potential Capacitance
(a) Constant Constant
Decrease
(b) Increase Increase Decrease
(c) Constant Decrease Increase
(d) Constant Increase Decrease
Q.5 A 500 mF capacitor is charged at a steady rate of 100mC/s. The potential difference across the capacitor will be
10V after an interval
(a) 5s (b) 20s (c) 25s (d) 50s
Q.6 A 1mF capacitor and 2mF capacitor are connected in parallel across a 1200V line.
The charged capacitors are then disconnected from the line and from each other.
These two capacitors are now connected to each other in parallel with terminals
of unlike signs together. The charges on the capacitors will be
(a) 1800mC each (b) 400mC
and 800mC
(c) 800mC and 400mC (d)
800mC and 800mC
Q.7 In a charged
capacitor, the energy resides in
(a) the positive
charges
(b) both the
positive and negative charges
(c) the field
between the plates
(d) around the
edges of capacitor plate
Q.8 A parallel plate
capacitor is charged to 160V. When a 2 mm thick dielectric slab is inserted in
between the plates the potential difference across the plates decreases,
however if the distance between the plates is increased by 1.6mm, the same
potential difference is restored. The dielectric constant of the material of
the slab is
(a) 1.25 (b) 2.5 (c) 4 (d) 5
Q.9 Two capacitors
each having capacitance C and
breakdown voltage V are joined in
series. The capacitance and breakdown voltage of combination is
(a) 2C and 2V (b) C/2
and V/2 (c) 2 C and V (d)
C/2
and 2V
Q.10 A parallel plate
capacitor of plate area A and plate
separation d is charged to potential
difference V and then the battery is disconnected. A slab of dielectric
constant K is then inserted between
the plates of the capacitor so as to fill the space between the plates. If Q, E
and W denote respectively, the
magnitude of charge on each plate, the electric field between the plates (after
the slab is inserted), and work done on the system in question in the process
of inserting the slab, then
(a) Q = e0AV / d (b) Q
= e0 KAV / d
(c) E = v/K d (d) W = e0AV2 / 2d (1-1/K)
Q.11 A parallel plate
air capacitor is connected to a battery. The quantities charge, voltage,
electric field and energy associated with this capacitor are given by Q0, V0, E0
and U0 respectively. A
dielectric slab is now introduced to fill the space between the plates with
battery still in connection. The corresponding quantities now given by Q, V,
E and U are related of the previous one as
(a) Q >Q0 (b) V>V0 (c) E
>E0 (d) U
>U0
Q.12 The amount of heat
liberated when a capacitor of C
farads charges to a potential difference of V
volts is discharged through a resistor of R
ohms is H joules. The same capacitor
is now charged to a potential difference of 2V and discharged through a
resistor of 2R ohms, then heat
liberated is
(a) 4H (b) 2H (c) H (d) H/2
Q.13 The heat
generated through 2W and 8W resistance separately when a capacitor of
200mF capacity charged to 200V is discharged one
– by – one will be
(a) 4J and 16J
respectively (b) 16J and 4J respectively
(c) 4J and 8J
respectively (d)
4J and 4J respectively
Q.14 Six identical capacitors each of 1mF are joined is parallel and the combination is put across
a battery of emf 2V. Now the battery is disconnected and the
capacitors are joined is series. The total energy and potential difference
across the series combination is
(a) 2mJ and 2V (b)
2mJ and 12V (c)
12mJ and 2V (d) 12mJ and 12V
Q.15 Suppose n identical capacitors are joined in
parallel and charged to potential V.
Now they are separated and joined in series. If the energy possessed by each
capacitor is U, then on joining them
in series, the energy and potential difference for the combination are
(a) nU,
V (b) U,
n V (c) nU,
nV (d) less than nU, nV
Q.16 A parallel plate capacitor with a dielectric
constant K=3 filling the space
between the plates is charged to a potential difference V. The battery is then disconnected and the dielectric slab having K=2. The ratio of energy stored in the
capacitor before and after replacing the dielectric slab by now one is
(a) 3 : 2 (b) 9 : 4 (c) 4 : 9 (d)
2 : 3
Q.17 A capacitor of capacity C1 is charged to a potential V0. The electrostatic energy stored in it is U0. It is connected to
another unchanged capacitor of capacitance C2
in parallel. The energy dissipated in the process is
(a) C2 / C1+C2 U0
(b) C1
/ C1+C2 U0
(c) [C1- C2 / C1 + C2]2
U0 (d) C1
C2 / 2 (C1 + C2)U0
Q.18 A parallel plate
capacitor is connected to a battery. The plates are pulled apart with a uniform
speed. If x is the separation between the plates then the time rate of change
of electrostatic energy of the capacitor is proportional to
(a) x2 (b) x (c)
1/x (d)
1/x2
Q.19 If we treat the earth as a conducting sphere
of radius 6400km, its capacitance would be of the order of
(a) 1mF (b) 1mF (c) 1F (d) 103F
Q.20 When two uncharged metal balls of radius
0.09 mm each collide, one electron is transferred between them. The potential
difference between them would be
(a) 16mV (b) 16pV (c) 32mV (d) 32pV
Q.21 A conducting sphere of radius R, and
carrying Q, is joined to an uncharged conducting sphere of radius 2R. The
charge flowing between them will be
(a) Q/4 (b) Q/3 (c) Q/2 (d) 2Q/3
Q.22 A capacitor of capacitance C is charged to a
potential difference V form a cell and then disconnected from it. A charge +Q
is now given to its positive plate. The potential difference across the
capacitor is now
(a) V (b) V+ Q/C
(c) V+Q/2C (d) V –Q/C, if V
Q.23 A capacitor is connected to a cell of emf ℰ
and some internal resistance. The potential difference across the
(a) cell
is ℰ (b) cell is < ℰ
(c) capacitor
is <ℰ (d) capacitor is >ℰ
Q.24 In a parallel –plate capacitor of
capacitance C, a metal sheet is inserted between the plates, parallel to them.
The thickness of the sheet is half of the separation between the plates. The
capacitance now becomes
(a) 4C (b) 2C (c) C/2 (d) C/4
Q.25 Two capacitors of capacitance 3mF and 6mF are charged to a potential of 12V each. They are now
connected to each other, with the positive plate of each joined to the negative
plate of the other. The potential difference across each will be
(a) zero (b) 3V (c) 4V (d) 6V
Q.26 Let ua
and ud represent the
energy density (energy per unit volume) in air and in a dielectric
respectively, for the same field in both. Let K = dielectric constant. Then,
(a) ua= ud (b) ua=
Kud (c) ud
= Kua (d) ua=(K-1) ud
Q.27 In a parallel –plate capacitor, the region between the plates is filled by a
dielectric slab. The capacitor is charged from a cell and then disconnected
from it. The slab is now taken out
(a) some
charge is drawn from the cell
(b) some
charge is returned to the cell
(c) the
potential difference across the capacitor is reduced
(d) no work
is done by an external agent in taking the slab out
Q.28 In a parallel –plate capacitor, the region
between the plates is filed by a dielectric slab. The capacitor is charge from
a cell and then disconnected from it. The slab is now taken out
(a) the
potential difference across the capacitor is reduced
(b) the
potential difference across the capacitor is increased
(c) the
energy stored in the capacitor is reduced
(d) no work is done by an external agent in taking
the slab out
Q.29 In order to obtain a time
constant of 10 seconds in an RC circuit containing a resistance of 103
W, the capacity of a condenser should be :
(a) 10mF (b) 100mF (c) 1000mF (d) 10,000mF.
Q.30 A parallel plate
capacitor is connected to a battery. The plates are pulled apart with a uniform
speed. If x is the separation between the plates then the time rate of change
of electrostatic energy of the capacitor is proportional to
(a) x2 (b) x (c) 1/x (d) 1/x2
ANSWER
Capacitor
1.
|
(b)
|
2.
|
(c)
|
3.
|
(b)
|
4.
|
(d)
|
5.
|
(d)
|
6.
|
(b)
|
7.
|
(c)
|
8.
|
(d)
|
9.
|
(a), (c), (d)
|
10.
|
(a), (d)
|
11.
|
(d)
|
12.
|
(a)
|
13.
|
(d)
|
14.
|
(d)
|
15.
|
(c)
|
16.
|
(d)
|
17.
|
(a)
|
18.
|
(d)
|
19.
|
(b)
|
20.
|
(c)
|
21.
|
(d)
|
22.
|
(d)
|
23.
|
(d)
|
24.
|
(a,c,d)
|
25.
|
(a)
|
26.
|
(c)
|
27.
|
(b)
|
28.
|
(b)
|
29.
|
(d)
|
30.
|
(d)
|
No comments:
Post a Comment