DC Pandey Solutions (JEE Main): Electrostatic- 2 | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


Exercises 
For JEE Main 
Objective Questions 
  Single Correct Option 
Q 1.  Units of electric flux are 
 (a) 
2
2
Nm
C
?
   (b) 
22
N
Cm ?
   (c) volt-m   (d) volt-m
3
 
Q 2.  A neutral pendulum oscillates in an uniform electric field as shown in figure. If a positive charge 
is given to the pendulum then its time period 
 
  (a) will increase (b) will decrease (c) will remain constant 
  (d) will first increase then decrease 
Q 3.  Identify the correct statement about the charges q
1
 and q
2 
 
  (a) q
1
 and q
2
 both are positive   (b) q
1
 and q
2
 both are negative 
  (c) q
1
 is positive q
2
 is negative  (d) q
2
 is positive and q
1
 is negative 
Q 4.  Three identical charges are placed at corners of an equilateral triangle of side l.If force between 
any two charges is F, the work required to double the dimensions of triangle is 
  (a) -3Fl   (b) 3Fl   (c) (-3/2) Fl   (d) (3/2) Fl 
Q 5.  A proton, a deuteron and an alpha particle are accelerated through potentials of V, 2 V and 4 V 
respectively. Their velocity will bear a ratio 
  (a) 1 : 1 : 1  (b) 1 : 2 : 1  (c) 2 : 1 : 1  (d) 1 : 1 : 2 
Q 6.  Electric potential at a point P, r distance away due to a point charge q at point A is V. If twice of 
this charge is distributed uniformly on the surface of a hollow sphere of radius 4rwith centre at 
point A, the potential at P now is 
  (a) V    (b) V/2   (c) V/4   (d) V/8 
Q 7.  Four charges +q, -q, + q and - q are placed in order on the four consecutive corners of a square of 
side a. The work done in interchanging the positions of any two neighbouring charges of the 
opposite sign is 
 (a) 
2
0
q
( 4 2)
4a
??
??
  (b) 
2
0
q
(4 2 2)
4a
?
??
  (c) 
2
0
q
(4 2 2)
4a
?
??
  (d) 
2
0
q
(4 2)
4a
?
??
  
Page 2


Exercises 
For JEE Main 
Objective Questions 
  Single Correct Option 
Q 1.  Units of electric flux are 
 (a) 
2
2
Nm
C
?
   (b) 
22
N
Cm ?
   (c) volt-m   (d) volt-m
3
 
Q 2.  A neutral pendulum oscillates in an uniform electric field as shown in figure. If a positive charge 
is given to the pendulum then its time period 
 
  (a) will increase (b) will decrease (c) will remain constant 
  (d) will first increase then decrease 
Q 3.  Identify the correct statement about the charges q
1
 and q
2 
 
  (a) q
1
 and q
2
 both are positive   (b) q
1
 and q
2
 both are negative 
  (c) q
1
 is positive q
2
 is negative  (d) q
2
 is positive and q
1
 is negative 
Q 4.  Three identical charges are placed at corners of an equilateral triangle of side l.If force between 
any two charges is F, the work required to double the dimensions of triangle is 
  (a) -3Fl   (b) 3Fl   (c) (-3/2) Fl   (d) (3/2) Fl 
Q 5.  A proton, a deuteron and an alpha particle are accelerated through potentials of V, 2 V and 4 V 
respectively. Their velocity will bear a ratio 
  (a) 1 : 1 : 1  (b) 1 : 2 : 1  (c) 2 : 1 : 1  (d) 1 : 1 : 2 
Q 6.  Electric potential at a point P, r distance away due to a point charge q at point A is V. If twice of 
this charge is distributed uniformly on the surface of a hollow sphere of radius 4rwith centre at 
point A, the potential at P now is 
  (a) V    (b) V/2   (c) V/4   (d) V/8 
Q 7.  Four charges +q, -q, + q and - q are placed in order on the four consecutive corners of a square of 
side a. The work done in interchanging the positions of any two neighbouring charges of the 
opposite sign is 
 (a) 
2
0
q
( 4 2)
4a
??
??
  (b) 
2
0
q
(4 2 2)
4a
?
??
  (c) 
2
0
q
(4 2 2)
4a
?
??
  (d) 
2
0
q
(4 2)
4a
?
??
  
Q 8.  Two concentric spheres of radii R and 2R are charged. The inner sphere has a charge of 1 ?C and 
the outer sphere has a charge of 2 ?C of the same sign. The potential is 9000 V at a distance 3R 
from the common centre. The value of R is 
  (a) 1 m   (b) 2 m   (c) 3 m   (d) 4 m 
Q 9.  A ring of radius R is having two charges q and 2q distributed on its two half parts. The electric 
potential at a point on its axis at a distance of 22 R
 
from its centre is 
0
1
k
4
?
??
 
 (a) 
3kq
R
   (b) 
kq
3R
   (c) 
kq
R
   (d) 
kq
3R
 
Q 10.  A particle A having a charge of 2.0 × 10
-6
 C and a mass of 100 g is fixed at the bottom of a smooth 
inclined plane of inclination 30°. Where should another particle B having same charge and mass, 
be placed on the inclined plane so that B may remain in equilibrium? 
  (a) 8 cm from the bottom    (b) 13 cm from the bottom 
  (c) 21 cm from the bottom    (d) 27 cm from the bottom 
Q 11.  Four positive charges ( 2 2 1 ? )Q
 
are arranged at the four corner of a square. Another charge q is 
placed at the centre of the square. Resulting force acting on each corner charge is zero if q is 
  (a) 
7Q
4
?   (b) 
4Q
7
?   (c) –Q   (d) ( 2 1)Q ?? 
Q 12.  A proton is released from rest, 10 cm from a charged sheet carrying charged density of - 2.21×10
-9
 
C/m
2
. It will strike the sheet after the time (approximately) 
  (a) 4 ?s   (b) 2 ?s   (c) 22 ?s  (d) 42 ?s 
Q 13.  Two point charges +q and -q are placed a distance x apart. A third charge is so placed that all the 
three charges are in equilibrium. Then 
  (a) unknown charge is -4q/9   (b) unknown charge is - 9q/4 
  (c) it should be at (x/3) from smaller charge between them 
  (d) None of the above 
Q 14.  Charges 2q and - q are placed at (a, 0) and (-a, 0) as shown in the figure. The coordinates of the 
point at which electric field intensity is zero will be (x, 0) where 
 
  (a) - a < x < a   (b) x < - a  (c) x > -a   (d) 0 < x < a 
Q 15.  Five point charges (+ q each) are placed at the five vertices of a regular hexagon of side 2a. What 
is the magnitude of the net electric field at the centre of the hexagon? 
 (a) 
2
0
1q
4a ??
   (b) 
2
0
q
16 a ??
   (c) 
2
0
2q
4a ??
   (d) 
2
0
5q
16 a ??
 
Q 16.  Two identical small conducting spheres having unequal positive charges q
1
 and q
2
 are separated by 
a distance r. If they are now made to touch each other and then separated again to the same 
distance, the electrostatic force between them in this case will be 
  (a) less than before  (b) same as before  (c) more than before  (d) zero 
Page 3


Exercises 
For JEE Main 
Objective Questions 
  Single Correct Option 
Q 1.  Units of electric flux are 
 (a) 
2
2
Nm
C
?
   (b) 
22
N
Cm ?
   (c) volt-m   (d) volt-m
3
 
Q 2.  A neutral pendulum oscillates in an uniform electric field as shown in figure. If a positive charge 
is given to the pendulum then its time period 
 
  (a) will increase (b) will decrease (c) will remain constant 
  (d) will first increase then decrease 
Q 3.  Identify the correct statement about the charges q
1
 and q
2 
 
  (a) q
1
 and q
2
 both are positive   (b) q
1
 and q
2
 both are negative 
  (c) q
1
 is positive q
2
 is negative  (d) q
2
 is positive and q
1
 is negative 
Q 4.  Three identical charges are placed at corners of an equilateral triangle of side l.If force between 
any two charges is F, the work required to double the dimensions of triangle is 
  (a) -3Fl   (b) 3Fl   (c) (-3/2) Fl   (d) (3/2) Fl 
Q 5.  A proton, a deuteron and an alpha particle are accelerated through potentials of V, 2 V and 4 V 
respectively. Their velocity will bear a ratio 
  (a) 1 : 1 : 1  (b) 1 : 2 : 1  (c) 2 : 1 : 1  (d) 1 : 1 : 2 
Q 6.  Electric potential at a point P, r distance away due to a point charge q at point A is V. If twice of 
this charge is distributed uniformly on the surface of a hollow sphere of radius 4rwith centre at 
point A, the potential at P now is 
  (a) V    (b) V/2   (c) V/4   (d) V/8 
Q 7.  Four charges +q, -q, + q and - q are placed in order on the four consecutive corners of a square of 
side a. The work done in interchanging the positions of any two neighbouring charges of the 
opposite sign is 
 (a) 
2
0
q
( 4 2)
4a
??
??
  (b) 
2
0
q
(4 2 2)
4a
?
??
  (c) 
2
0
q
(4 2 2)
4a
?
??
  (d) 
2
0
q
(4 2)
4a
?
??
  
Q 8.  Two concentric spheres of radii R and 2R are charged. The inner sphere has a charge of 1 ?C and 
the outer sphere has a charge of 2 ?C of the same sign. The potential is 9000 V at a distance 3R 
from the common centre. The value of R is 
  (a) 1 m   (b) 2 m   (c) 3 m   (d) 4 m 
Q 9.  A ring of radius R is having two charges q and 2q distributed on its two half parts. The electric 
potential at a point on its axis at a distance of 22 R
 
from its centre is 
0
1
k
4
?
??
 
 (a) 
3kq
R
   (b) 
kq
3R
   (c) 
kq
R
   (d) 
kq
3R
 
Q 10.  A particle A having a charge of 2.0 × 10
-6
 C and a mass of 100 g is fixed at the bottom of a smooth 
inclined plane of inclination 30°. Where should another particle B having same charge and mass, 
be placed on the inclined plane so that B may remain in equilibrium? 
  (a) 8 cm from the bottom    (b) 13 cm from the bottom 
  (c) 21 cm from the bottom    (d) 27 cm from the bottom 
Q 11.  Four positive charges ( 2 2 1 ? )Q
 
are arranged at the four corner of a square. Another charge q is 
placed at the centre of the square. Resulting force acting on each corner charge is zero if q is 
  (a) 
7Q
4
?   (b) 
4Q
7
?   (c) –Q   (d) ( 2 1)Q ?? 
Q 12.  A proton is released from rest, 10 cm from a charged sheet carrying charged density of - 2.21×10
-9
 
C/m
2
. It will strike the sheet after the time (approximately) 
  (a) 4 ?s   (b) 2 ?s   (c) 22 ?s  (d) 42 ?s 
Q 13.  Two point charges +q and -q are placed a distance x apart. A third charge is so placed that all the 
three charges are in equilibrium. Then 
  (a) unknown charge is -4q/9   (b) unknown charge is - 9q/4 
  (c) it should be at (x/3) from smaller charge between them 
  (d) None of the above 
Q 14.  Charges 2q and - q are placed at (a, 0) and (-a, 0) as shown in the figure. The coordinates of the 
point at which electric field intensity is zero will be (x, 0) where 
 
  (a) - a < x < a   (b) x < - a  (c) x > -a   (d) 0 < x < a 
Q 15.  Five point charges (+ q each) are placed at the five vertices of a regular hexagon of side 2a. What 
is the magnitude of the net electric field at the centre of the hexagon? 
 (a) 
2
0
1q
4a ??
   (b) 
2
0
q
16 a ??
   (c) 
2
0
2q
4a ??
   (d) 
2
0
5q
16 a ??
 
Q 16.  Two identical small conducting spheres having unequal positive charges q
1
 and q
2
 are separated by 
a distance r. If they are now made to touch each other and then separated again to the same 
distance, the electrostatic force between them in this case will be 
  (a) less than before  (b) same as before  (c) more than before  (d) zero 
Q 17.  Three concentric conducting spherical shells carry charges + 4Q on the inner shell - 2Q on the 
middle shell and + 6Q on the outer shell. The charge on the inner surface of the outer shell is 
  (a) 0    (b) 4Q    (c) -Q    (d) -2Q 
Q 18.  1000 drops of same size are charged to a potential of 1 V each. If they coalesce to form a single 
drop, its potential would be 
  (a) V    (b) 10 V   (c) 100 V   (d) 1000 V 
Q 19.  Two concentric conducting spheres of radii R and 2R are carrying charges Q and -2Q respectively. 
If the charge on inner sphere is doubled, the potential difference between the two spheres will 
 
  (a) become two times    (b) become four times 
  (c) be halved     (d) remain same 
Q 20.  Charges Q, 2Q and - Q are given to three concentric conducting spherical shells A, B and C 
respectively as shown in figure. The ratio of charges on the inner and outer
 
surfaces of shell C will 
be 
 
 (a) 
3
4
?   (b) 
3
4
?
   (c) 
3
2
    (d) 
3
2
?
 
Q 21.  The electric field in a region of space is given by 
ˆˆ
E 5i 2j N/ C ??
?
.
 
The flux of E
?
 
due to this field 
through an area 1 m
2
 lying in the y-z plane, in SI units, is 
  (a) 5    (b) 10    (c) 2    (d) 5 29 
Q 22.  A charge Q is placed at each of the two opposite corners of a square. A charge q is placed at each 
of the other two corners. If the resultant force on each charge q is zero, then 
 (a) q 2Q ?   (b) q 2Q ??   (c) q 2 2Q ?   (d) q 2 2Q ?? 
Q 23.  A and B are two concentric spherical shells. If A is given a charge + q while B is earthed as shown 
in figure, then 
 
  (a) charge on the outer surface of shell B is zero 
  (b) the charge on B is equal and opposite to that of A 
Page 4


Exercises 
For JEE Main 
Objective Questions 
  Single Correct Option 
Q 1.  Units of electric flux are 
 (a) 
2
2
Nm
C
?
   (b) 
22
N
Cm ?
   (c) volt-m   (d) volt-m
3
 
Q 2.  A neutral pendulum oscillates in an uniform electric field as shown in figure. If a positive charge 
is given to the pendulum then its time period 
 
  (a) will increase (b) will decrease (c) will remain constant 
  (d) will first increase then decrease 
Q 3.  Identify the correct statement about the charges q
1
 and q
2 
 
  (a) q
1
 and q
2
 both are positive   (b) q
1
 and q
2
 both are negative 
  (c) q
1
 is positive q
2
 is negative  (d) q
2
 is positive and q
1
 is negative 
Q 4.  Three identical charges are placed at corners of an equilateral triangle of side l.If force between 
any two charges is F, the work required to double the dimensions of triangle is 
  (a) -3Fl   (b) 3Fl   (c) (-3/2) Fl   (d) (3/2) Fl 
Q 5.  A proton, a deuteron and an alpha particle are accelerated through potentials of V, 2 V and 4 V 
respectively. Their velocity will bear a ratio 
  (a) 1 : 1 : 1  (b) 1 : 2 : 1  (c) 2 : 1 : 1  (d) 1 : 1 : 2 
Q 6.  Electric potential at a point P, r distance away due to a point charge q at point A is V. If twice of 
this charge is distributed uniformly on the surface of a hollow sphere of radius 4rwith centre at 
point A, the potential at P now is 
  (a) V    (b) V/2   (c) V/4   (d) V/8 
Q 7.  Four charges +q, -q, + q and - q are placed in order on the four consecutive corners of a square of 
side a. The work done in interchanging the positions of any two neighbouring charges of the 
opposite sign is 
 (a) 
2
0
q
( 4 2)
4a
??
??
  (b) 
2
0
q
(4 2 2)
4a
?
??
  (c) 
2
0
q
(4 2 2)
4a
?
??
  (d) 
2
0
q
(4 2)
4a
?
??
  
Q 8.  Two concentric spheres of radii R and 2R are charged. The inner sphere has a charge of 1 ?C and 
the outer sphere has a charge of 2 ?C of the same sign. The potential is 9000 V at a distance 3R 
from the common centre. The value of R is 
  (a) 1 m   (b) 2 m   (c) 3 m   (d) 4 m 
Q 9.  A ring of radius R is having two charges q and 2q distributed on its two half parts. The electric 
potential at a point on its axis at a distance of 22 R
 
from its centre is 
0
1
k
4
?
??
 
 (a) 
3kq
R
   (b) 
kq
3R
   (c) 
kq
R
   (d) 
kq
3R
 
Q 10.  A particle A having a charge of 2.0 × 10
-6
 C and a mass of 100 g is fixed at the bottom of a smooth 
inclined plane of inclination 30°. Where should another particle B having same charge and mass, 
be placed on the inclined plane so that B may remain in equilibrium? 
  (a) 8 cm from the bottom    (b) 13 cm from the bottom 
  (c) 21 cm from the bottom    (d) 27 cm from the bottom 
Q 11.  Four positive charges ( 2 2 1 ? )Q
 
are arranged at the four corner of a square. Another charge q is 
placed at the centre of the square. Resulting force acting on each corner charge is zero if q is 
  (a) 
7Q
4
?   (b) 
4Q
7
?   (c) –Q   (d) ( 2 1)Q ?? 
Q 12.  A proton is released from rest, 10 cm from a charged sheet carrying charged density of - 2.21×10
-9
 
C/m
2
. It will strike the sheet after the time (approximately) 
  (a) 4 ?s   (b) 2 ?s   (c) 22 ?s  (d) 42 ?s 
Q 13.  Two point charges +q and -q are placed a distance x apart. A third charge is so placed that all the 
three charges are in equilibrium. Then 
  (a) unknown charge is -4q/9   (b) unknown charge is - 9q/4 
  (c) it should be at (x/3) from smaller charge between them 
  (d) None of the above 
Q 14.  Charges 2q and - q are placed at (a, 0) and (-a, 0) as shown in the figure. The coordinates of the 
point at which electric field intensity is zero will be (x, 0) where 
 
  (a) - a < x < a   (b) x < - a  (c) x > -a   (d) 0 < x < a 
Q 15.  Five point charges (+ q each) are placed at the five vertices of a regular hexagon of side 2a. What 
is the magnitude of the net electric field at the centre of the hexagon? 
 (a) 
2
0
1q
4a ??
   (b) 
2
0
q
16 a ??
   (c) 
2
0
2q
4a ??
   (d) 
2
0
5q
16 a ??
 
Q 16.  Two identical small conducting spheres having unequal positive charges q
1
 and q
2
 are separated by 
a distance r. If they are now made to touch each other and then separated again to the same 
distance, the electrostatic force between them in this case will be 
  (a) less than before  (b) same as before  (c) more than before  (d) zero 
Q 17.  Three concentric conducting spherical shells carry charges + 4Q on the inner shell - 2Q on the 
middle shell and + 6Q on the outer shell. The charge on the inner surface of the outer shell is 
  (a) 0    (b) 4Q    (c) -Q    (d) -2Q 
Q 18.  1000 drops of same size are charged to a potential of 1 V each. If they coalesce to form a single 
drop, its potential would be 
  (a) V    (b) 10 V   (c) 100 V   (d) 1000 V 
Q 19.  Two concentric conducting spheres of radii R and 2R are carrying charges Q and -2Q respectively. 
If the charge on inner sphere is doubled, the potential difference between the two spheres will 
 
  (a) become two times    (b) become four times 
  (c) be halved     (d) remain same 
Q 20.  Charges Q, 2Q and - Q are given to three concentric conducting spherical shells A, B and C 
respectively as shown in figure. The ratio of charges on the inner and outer
 
surfaces of shell C will 
be 
 
 (a) 
3
4
?   (b) 
3
4
?
   (c) 
3
2
    (d) 
3
2
?
 
Q 21.  The electric field in a region of space is given by 
ˆˆ
E 5i 2j N/ C ??
?
.
 
The flux of E
?
 
due to this field 
through an area 1 m
2
 lying in the y-z plane, in SI units, is 
  (a) 5    (b) 10    (c) 2    (d) 5 29 
Q 22.  A charge Q is placed at each of the two opposite corners of a square. A charge q is placed at each 
of the other two corners. If the resultant force on each charge q is zero, then 
 (a) q 2Q ?   (b) q 2Q ??   (c) q 2 2Q ?   (d) q 2 2Q ?? 
Q 23.  A and B are two concentric spherical shells. If A is given a charge + q while B is earthed as shown 
in figure, then 
 
  (a) charge on the outer surface of shell B is zero 
  (b) the charge on B is equal and opposite to that of A 
  (c) the field inside A and outside B is zero 
  (d) All of the above 
Q 24. A solid sphere of radius R has charge 'q' uniformly distributed over its volume. The distance from 
its surface at which the electrostatic potential is equal to half of the potential at the centre is 
(a) R    (b) 2R   (c) 
R
3
    (d) 
R
2
 
Q 25.  Four dipoles each of magnitudes of charges ?e are placed inside a sphere. The total flux of E
?
 
coming out of the sphere is 
 (a) zero  (b) 
0
4e
?
   (c) 
0
8e
?
    (d) None of these  
Q 26.  A pendulum bob of mass m carrying a charge q is at rest with its string making an angle with the 
vertical in a uniform horizontal electric field E. The tension in the string is 
 (a) 
mg
sin ?
   (b) mg   (c) 
qE
sin ?
   (d) 
qE
cos ?
 
Q 27.  Two isolated, charged conducting spheres of radii a and b produce the same electric field near 
their surfaces. The ratio of electric potentials on their surfaces is 
 (a) 
a
b
    (b) 
b
a
   (c) 
2
2
a
b
   (d) 
2
2
b
a
 
Q 28.  Two point charges + q and - q are held fixed at (- a, 0) and (a, 0) respectively of a x-y coordinate 
system, then 
  (a) the electric field E
?
at all points on the x-axis has the same direction 
  (b) 
E
?
 at all points on the y-axis is along 
ˆ
i 
  (c) positive work is done in bringing a test charge from infinity to the origin 
  (d) All of the above 
Q 29.  A conducting shell S
1
 having a charge Q is surrounded by an uncharged concentric conducting 
spherical shell S
2
. Let the potential difference between S
1
 and that S
2
 be V. If the shell S
2
 is now 
given a charge -3Q, the new potential difference between the same two shells is 
  (a) V    (b) 2V    (c) 4 V   (d) -2V 
Q 30.  At a certain distance from a point charge, the field intensity is 500 V/m and the potential is - 3000 
V The distance to the charge and the magnitude of the charge respectively are 
  (a) 6m and 6 ?C  (b) 4m and 2 ?C  (c) 6m and 4 ?C  (d) 6m and 2 ?C 
Q 31.  Two point charges q
1
 and q
2
 are placed at a distance of 50 m from each other in air, and interact 
with a certain force. The same charges are now put in oil whose relative permittivity is 5. If the 
interacting force between them is still the same, their separation now is  
  (a) 16.6 m   (b) 22.3 m   (c) 28.4 m   (d) 25.0 cm 
Q 32.  An infinite line of charge ? per unit length is placed along the y-axis. The work done in moving a 
charge q from A(a, 0) to B(2a, 0) is 
  (a) 
0
q
ln 2
4
?
??
   (b) 
0
q1
ln
22
? ??
??
??
??
  (c) 
0
q
ln 2
4
?
??
  (d) 
0
q
ln 2
4
?
??
 
Page 5


Exercises 
For JEE Main 
Objective Questions 
  Single Correct Option 
Q 1.  Units of electric flux are 
 (a) 
2
2
Nm
C
?
   (b) 
22
N
Cm ?
   (c) volt-m   (d) volt-m
3
 
Q 2.  A neutral pendulum oscillates in an uniform electric field as shown in figure. If a positive charge 
is given to the pendulum then its time period 
 
  (a) will increase (b) will decrease (c) will remain constant 
  (d) will first increase then decrease 
Q 3.  Identify the correct statement about the charges q
1
 and q
2 
 
  (a) q
1
 and q
2
 both are positive   (b) q
1
 and q
2
 both are negative 
  (c) q
1
 is positive q
2
 is negative  (d) q
2
 is positive and q
1
 is negative 
Q 4.  Three identical charges are placed at corners of an equilateral triangle of side l.If force between 
any two charges is F, the work required to double the dimensions of triangle is 
  (a) -3Fl   (b) 3Fl   (c) (-3/2) Fl   (d) (3/2) Fl 
Q 5.  A proton, a deuteron and an alpha particle are accelerated through potentials of V, 2 V and 4 V 
respectively. Their velocity will bear a ratio 
  (a) 1 : 1 : 1  (b) 1 : 2 : 1  (c) 2 : 1 : 1  (d) 1 : 1 : 2 
Q 6.  Electric potential at a point P, r distance away due to a point charge q at point A is V. If twice of 
this charge is distributed uniformly on the surface of a hollow sphere of radius 4rwith centre at 
point A, the potential at P now is 
  (a) V    (b) V/2   (c) V/4   (d) V/8 
Q 7.  Four charges +q, -q, + q and - q are placed in order on the four consecutive corners of a square of 
side a. The work done in interchanging the positions of any two neighbouring charges of the 
opposite sign is 
 (a) 
2
0
q
( 4 2)
4a
??
??
  (b) 
2
0
q
(4 2 2)
4a
?
??
  (c) 
2
0
q
(4 2 2)
4a
?
??
  (d) 
2
0
q
(4 2)
4a
?
??
  
Q 8.  Two concentric spheres of radii R and 2R are charged. The inner sphere has a charge of 1 ?C and 
the outer sphere has a charge of 2 ?C of the same sign. The potential is 9000 V at a distance 3R 
from the common centre. The value of R is 
  (a) 1 m   (b) 2 m   (c) 3 m   (d) 4 m 
Q 9.  A ring of radius R is having two charges q and 2q distributed on its two half parts. The electric 
potential at a point on its axis at a distance of 22 R
 
from its centre is 
0
1
k
4
?
??
 
 (a) 
3kq
R
   (b) 
kq
3R
   (c) 
kq
R
   (d) 
kq
3R
 
Q 10.  A particle A having a charge of 2.0 × 10
-6
 C and a mass of 100 g is fixed at the bottom of a smooth 
inclined plane of inclination 30°. Where should another particle B having same charge and mass, 
be placed on the inclined plane so that B may remain in equilibrium? 
  (a) 8 cm from the bottom    (b) 13 cm from the bottom 
  (c) 21 cm from the bottom    (d) 27 cm from the bottom 
Q 11.  Four positive charges ( 2 2 1 ? )Q
 
are arranged at the four corner of a square. Another charge q is 
placed at the centre of the square. Resulting force acting on each corner charge is zero if q is 
  (a) 
7Q
4
?   (b) 
4Q
7
?   (c) –Q   (d) ( 2 1)Q ?? 
Q 12.  A proton is released from rest, 10 cm from a charged sheet carrying charged density of - 2.21×10
-9
 
C/m
2
. It will strike the sheet after the time (approximately) 
  (a) 4 ?s   (b) 2 ?s   (c) 22 ?s  (d) 42 ?s 
Q 13.  Two point charges +q and -q are placed a distance x apart. A third charge is so placed that all the 
three charges are in equilibrium. Then 
  (a) unknown charge is -4q/9   (b) unknown charge is - 9q/4 
  (c) it should be at (x/3) from smaller charge between them 
  (d) None of the above 
Q 14.  Charges 2q and - q are placed at (a, 0) and (-a, 0) as shown in the figure. The coordinates of the 
point at which electric field intensity is zero will be (x, 0) where 
 
  (a) - a < x < a   (b) x < - a  (c) x > -a   (d) 0 < x < a 
Q 15.  Five point charges (+ q each) are placed at the five vertices of a regular hexagon of side 2a. What 
is the magnitude of the net electric field at the centre of the hexagon? 
 (a) 
2
0
1q
4a ??
   (b) 
2
0
q
16 a ??
   (c) 
2
0
2q
4a ??
   (d) 
2
0
5q
16 a ??
 
Q 16.  Two identical small conducting spheres having unequal positive charges q
1
 and q
2
 are separated by 
a distance r. If they are now made to touch each other and then separated again to the same 
distance, the electrostatic force between them in this case will be 
  (a) less than before  (b) same as before  (c) more than before  (d) zero 
Q 17.  Three concentric conducting spherical shells carry charges + 4Q on the inner shell - 2Q on the 
middle shell and + 6Q on the outer shell. The charge on the inner surface of the outer shell is 
  (a) 0    (b) 4Q    (c) -Q    (d) -2Q 
Q 18.  1000 drops of same size are charged to a potential of 1 V each. If they coalesce to form a single 
drop, its potential would be 
  (a) V    (b) 10 V   (c) 100 V   (d) 1000 V 
Q 19.  Two concentric conducting spheres of radii R and 2R are carrying charges Q and -2Q respectively. 
If the charge on inner sphere is doubled, the potential difference between the two spheres will 
 
  (a) become two times    (b) become four times 
  (c) be halved     (d) remain same 
Q 20.  Charges Q, 2Q and - Q are given to three concentric conducting spherical shells A, B and C 
respectively as shown in figure. The ratio of charges on the inner and outer
 
surfaces of shell C will 
be 
 
 (a) 
3
4
?   (b) 
3
4
?
   (c) 
3
2
    (d) 
3
2
?
 
Q 21.  The electric field in a region of space is given by 
ˆˆ
E 5i 2j N/ C ??
?
.
 
The flux of E
?
 
due to this field 
through an area 1 m
2
 lying in the y-z plane, in SI units, is 
  (a) 5    (b) 10    (c) 2    (d) 5 29 
Q 22.  A charge Q is placed at each of the two opposite corners of a square. A charge q is placed at each 
of the other two corners. If the resultant force on each charge q is zero, then 
 (a) q 2Q ?   (b) q 2Q ??   (c) q 2 2Q ?   (d) q 2 2Q ?? 
Q 23.  A and B are two concentric spherical shells. If A is given a charge + q while B is earthed as shown 
in figure, then 
 
  (a) charge on the outer surface of shell B is zero 
  (b) the charge on B is equal and opposite to that of A 
  (c) the field inside A and outside B is zero 
  (d) All of the above 
Q 24. A solid sphere of radius R has charge 'q' uniformly distributed over its volume. The distance from 
its surface at which the electrostatic potential is equal to half of the potential at the centre is 
(a) R    (b) 2R   (c) 
R
3
    (d) 
R
2
 
Q 25.  Four dipoles each of magnitudes of charges ?e are placed inside a sphere. The total flux of E
?
 
coming out of the sphere is 
 (a) zero  (b) 
0
4e
?
   (c) 
0
8e
?
    (d) None of these  
Q 26.  A pendulum bob of mass m carrying a charge q is at rest with its string making an angle with the 
vertical in a uniform horizontal electric field E. The tension in the string is 
 (a) 
mg
sin ?
   (b) mg   (c) 
qE
sin ?
   (d) 
qE
cos ?
 
Q 27.  Two isolated, charged conducting spheres of radii a and b produce the same electric field near 
their surfaces. The ratio of electric potentials on their surfaces is 
 (a) 
a
b
    (b) 
b
a
   (c) 
2
2
a
b
   (d) 
2
2
b
a
 
Q 28.  Two point charges + q and - q are held fixed at (- a, 0) and (a, 0) respectively of a x-y coordinate 
system, then 
  (a) the electric field E
?
at all points on the x-axis has the same direction 
  (b) 
E
?
 at all points on the y-axis is along 
ˆ
i 
  (c) positive work is done in bringing a test charge from infinity to the origin 
  (d) All of the above 
Q 29.  A conducting shell S
1
 having a charge Q is surrounded by an uncharged concentric conducting 
spherical shell S
2
. Let the potential difference between S
1
 and that S
2
 be V. If the shell S
2
 is now 
given a charge -3Q, the new potential difference between the same two shells is 
  (a) V    (b) 2V    (c) 4 V   (d) -2V 
Q 30.  At a certain distance from a point charge, the field intensity is 500 V/m and the potential is - 3000 
V The distance to the charge and the magnitude of the charge respectively are 
  (a) 6m and 6 ?C  (b) 4m and 2 ?C  (c) 6m and 4 ?C  (d) 6m and 2 ?C 
Q 31.  Two point charges q
1
 and q
2
 are placed at a distance of 50 m from each other in air, and interact 
with a certain force. The same charges are now put in oil whose relative permittivity is 5. If the 
interacting force between them is still the same, their separation now is  
  (a) 16.6 m   (b) 22.3 m   (c) 28.4 m   (d) 25.0 cm 
Q 32.  An infinite line of charge ? per unit length is placed along the y-axis. The work done in moving a 
charge q from A(a, 0) to B(2a, 0) is 
  (a) 
0
q
ln 2
4
?
??
   (b) 
0
q1
ln
22
? ??
??
??
??
  (c) 
0
q
ln 2
4
?
??
  (d) 
0
q
ln 2
4
?
??
 
Q 33.  An electric dipole is placed perpendicular to an infinite line of charge at some distance as shown 
in figure. Identify the correct statement. 
 
  (a) The dipole is attracted towards the line charge 
  (b) The dipole is repelled away from the line charge 
  (c) The dipole does not experience a force 
  (d) The dipole experiences a force as well as a torque 
Q 34.  An electrical charge 2 × 10
-8
 C is placed at the point (1,2,4)m. At the point (4, 2, 0) m, the electric 
(a) potential will be 36 V   (b) field will be along y-axis 
  (c) field will increase if the space between the points is filled with a dielectric 
  (d) All of the above 
Q 35.  If the potential at the centre of a uniformly charged hollow sphere of radius R is V then electric
 
field at a distance r from the centre of sphere will be (r > R ) 
 
  (a) 
2
VR
r
   (b) 
2
Vr
r
   (c) 
VR
r
   (d) 
22
VR
Rr ?
 
Q 36.  A and B are two concentric spheres. If A is given a charge Q while B is earthed as shown in 
figure, 
 
  (a) the charge density of A and B are same (b) the field inside and outside A is zero 
  (c) the field between A and B is not zero (d) the field inside and outside B is zero 
Q 37.  There is an electric field E in x-direction. If the work done on moving a charge of 0.2 C through a 
distance of 2 m along a line making an angle 60° with x-axis is 4 J, then what is the value of E? 
  (a) 3 N / C   (b) 4N/C  (c) 5N/C   (d) 20N/C 
Q 38.  Two thin wire rings each having radius R are placed at a distance d apart with their axes 
coinciding. The charges on the two rings are + Q and - Q. The potential difference between the 
centres of the two rings is 
 (a) zero     (b) 
22
0
Q 1 1
4R
Rd
??
?
??
??
?
??