Electrostatic Solved Examples | Physics for JEE Main & Advanced PDF Download

 Page 1


Solved Examples on Electrostatics 
JEE Mains 
Q1. The wedge-shaped surface in figure is in a region of uniform electric field ?? ?? 
along ?? axis. The net electric flux for the entire closed surface is 
(a) ?? ?? ?? 
(b) ???? ?? ?? 
(c) ???? ?? ?? 
(d) zero 
Ans: (d) Explanation: 
Since, field is uniform, the net flux for the closed surface is zero. 
Q2. A block of mass ?? carrying a positive charge ?? is placed on a smooth 
horizontal table, which ends in a vertical wall situated at a distance ?? from 
block. An electric field ?? is switched on towards right. Assuming 
elastic collisions, find the time period of resultant oscillation. 
(a) v
?? ?????? ?? 
(b) v
?????? ????
 
(c) v
?????? ????
 
(d) v
????
????
 
Ans: (b) Acceleration of the block a =
qE
m
 
d =
1
2
at
2
 
Required time = 2?? = v
8md
qE
 
 
 
Q3. Following operations can be performed on a capacitor. 
A: connect the capacitor to a battery of emf E. 
B: Disconnect the battery. 
C: Reconnect the battery with polarity reversed. 
D: Insert a dielectric slab into the capacitor. 
Now choose the incorrect option (s) 
(A) in action ?????? (perform ?? , then ?? and then ?? ), the stored electric energy 
remains unchanged and no thermal energy is developed. 
(B) the charge appearing on capacitor is greater after the action ADB than after 
the action ABD. 
(C) the electric energy stored in the capacitor is greater after the action ?????? 
than the action ?????? . 
(D) the electric field in the capacitor after the action ???? is same as that after the 
Page 2


Solved Examples on Electrostatics 
JEE Mains 
Q1. The wedge-shaped surface in figure is in a region of uniform electric field ?? ?? 
along ?? axis. The net electric flux for the entire closed surface is 
(a) ?? ?? ?? 
(b) ???? ?? ?? 
(c) ???? ?? ?? 
(d) zero 
Ans: (d) Explanation: 
Since, field is uniform, the net flux for the closed surface is zero. 
Q2. A block of mass ?? carrying a positive charge ?? is placed on a smooth 
horizontal table, which ends in a vertical wall situated at a distance ?? from 
block. An electric field ?? is switched on towards right. Assuming 
elastic collisions, find the time period of resultant oscillation. 
(a) v
?? ?????? ?? 
(b) v
?????? ????
 
(c) v
?????? ????
 
(d) v
????
????
 
Ans: (b) Acceleration of the block a =
qE
m
 
d =
1
2
at
2
 
Required time = 2?? = v
8md
qE
 
 
 
Q3. Following operations can be performed on a capacitor. 
A: connect the capacitor to a battery of emf E. 
B: Disconnect the battery. 
C: Reconnect the battery with polarity reversed. 
D: Insert a dielectric slab into the capacitor. 
Now choose the incorrect option (s) 
(A) in action ?????? (perform ?? , then ?? and then ?? ), the stored electric energy 
remains unchanged and no thermal energy is developed. 
(B) the charge appearing on capacitor is greater after the action ADB than after 
the action ABD. 
(C) the electric energy stored in the capacitor is greater after the action ?????? 
than the action ?????? . 
(D) the electric field in the capacitor after the action ???? is same as that after the 
action DA. 
Ans:(A) 
Use the concept of capacitor, charging, discharging etc. 
Q4. Gauss's law is frequently written in the following form: 
? ?? ?
. ?? ?? ?
=
?? mec 
?? ?? , 
Where, the symbols have their usual meanings 
(A) this law is true for all closed surfaces 
(B) it is true only in vacuum 
(C) it is true only when the charge distribution is symmetric 
(D) it is true only when the electric field is symmetric 
Ans: (A) 
Gauss's law is true for all closed surface. 
Q5. An electron of mass ?? ?? , initially at rest, moves through a certain distance in 
a uniform electric field in time ?? ?? . A proton of mass ?? ?? , also initially at rest, 
takes time ?? ?? to move through an equal distance in this uniform electric field. 
Neglecting the effect of gravity, the ratio ?? ?? /?? ?? is equal to 
(A) 1 
(B) (
?? ?? ?? ?? )
?? /?? 
(C) (
?? ?? ?? ?? )
?? /?? 
(D) (
?? ?? ?? ?? ) 
Ans. C 
Acceleration in uniform electric field 
a =
qE
m
 
If ?? is time for a distance ?? , 
d =
1
2
(
qE
m
)t
2
 
or, ?? = v
2????
????
 
So, 
t
1
t
2
=
v
m
c
m
p
 
 
 
Q6. If charges ?? /?? and ?? ?? are placed at the centre of face and at the corner of a 
cube, then the total flux through the cube will be 
(A) 
?? ?? ?? ?? 
(B) 
?? ?? ?? 
Page 3


Solved Examples on Electrostatics 
JEE Mains 
Q1. The wedge-shaped surface in figure is in a region of uniform electric field ?? ?? 
along ?? axis. The net electric flux for the entire closed surface is 
(a) ?? ?? ?? 
(b) ???? ?? ?? 
(c) ???? ?? ?? 
(d) zero 
Ans: (d) Explanation: 
Since, field is uniform, the net flux for the closed surface is zero. 
Q2. A block of mass ?? carrying a positive charge ?? is placed on a smooth 
horizontal table, which ends in a vertical wall situated at a distance ?? from 
block. An electric field ?? is switched on towards right. Assuming 
elastic collisions, find the time period of resultant oscillation. 
(a) v
?? ?????? ?? 
(b) v
?????? ????
 
(c) v
?????? ????
 
(d) v
????
????
 
Ans: (b) Acceleration of the block a =
qE
m
 
d =
1
2
at
2
 
Required time = 2?? = v
8md
qE
 
 
 
Q3. Following operations can be performed on a capacitor. 
A: connect the capacitor to a battery of emf E. 
B: Disconnect the battery. 
C: Reconnect the battery with polarity reversed. 
D: Insert a dielectric slab into the capacitor. 
Now choose the incorrect option (s) 
(A) in action ?????? (perform ?? , then ?? and then ?? ), the stored electric energy 
remains unchanged and no thermal energy is developed. 
(B) the charge appearing on capacitor is greater after the action ADB than after 
the action ABD. 
(C) the electric energy stored in the capacitor is greater after the action ?????? 
than the action ?????? . 
(D) the electric field in the capacitor after the action ???? is same as that after the 
action DA. 
Ans:(A) 
Use the concept of capacitor, charging, discharging etc. 
Q4. Gauss's law is frequently written in the following form: 
? ?? ?
. ?? ?? ?
=
?? mec 
?? ?? , 
Where, the symbols have their usual meanings 
(A) this law is true for all closed surfaces 
(B) it is true only in vacuum 
(C) it is true only when the charge distribution is symmetric 
(D) it is true only when the electric field is symmetric 
Ans: (A) 
Gauss's law is true for all closed surface. 
Q5. An electron of mass ?? ?? , initially at rest, moves through a certain distance in 
a uniform electric field in time ?? ?? . A proton of mass ?? ?? , also initially at rest, 
takes time ?? ?? to move through an equal distance in this uniform electric field. 
Neglecting the effect of gravity, the ratio ?? ?? /?? ?? is equal to 
(A) 1 
(B) (
?? ?? ?? ?? )
?? /?? 
(C) (
?? ?? ?? ?? )
?? /?? 
(D) (
?? ?? ?? ?? ) 
Ans. C 
Acceleration in uniform electric field 
a =
qE
m
 
If ?? is time for a distance ?? , 
d =
1
2
(
qE
m
)t
2
 
or, ?? = v
2????
????
 
So, 
t
1
t
2
=
v
m
c
m
p
 
 
 
Q6. If charges ?? /?? and ?? ?? are placed at the centre of face and at the corner of a 
cube, then the total flux through the cube will be 
(A) 
?? ?? ?? ?? 
(B) 
?? ?? ?? 
(C) 
?? ?? ?? ?? 
(D) 
?? ?? ?? ?? 
Ans: A 
Flux through the cube when ?? /2 is placed at the centre of face 
?? 1
=
?? /2
2?? 0
=
?? 4?? 0
 
Flux through the cube when 2?? is placed at the corner of cube is 
?? 2
=
2?? 8?? 0
=
?? 4?? 0
 
Now, total flux through the cube 
?? = ?? 1
+ ?? 2
=
q
2?? 0
 
Q7. A charge +?? is fixed at each of the points ?? = ?? ?? , ?? = ?? ?? ?? , ?? = ?? ?? ?? , … , 8 on the ?? -
axis and a charge -?? is fixed at each of the points ?? = ?? ?? ?? , ?? = ?? ?? ?? , ?? = ?? ?? ?? , … , 8. 
Here, ?? ?? is a positive quantity. Take the electric potential at a point due to 
charge ?? at a distance ?? from it to be 
?? ?? ?? ?? ?? ?? . Then, the potential at origin due to 
the above system of charges is 
(A) 0 
(B) 8 
(C) 
?? ?? ?? ?? ?? ?? ?? ???? ?? 
(D) 
?? ???? ?? ?? ?? ?? ?? ?? ?? 
Ans: D 
V =
q
4?? ?? 0
(
1
x
0
-
1
2x
0
+
1
3x
0
-
1
4x
0
+ ? ) =
q
4?? ?? 0
x
0
(1 -
1
2
+
1
3
-
1
4
+ ? ) =
q
4?? ?? 0
x
0
ln ( 2) 
 
Q8. Find the charge on an iron particle of mass ?? . ???????? , if ?? . ???? % of electrons are 
removed from it. 
(A) -?? . ???????????? 
(B) ?? . ???????????? 
(C) ?? . ?????? 
(D) ?? . ???? 
Ans: B 
Page 4


Solved Examples on Electrostatics 
JEE Mains 
Q1. The wedge-shaped surface in figure is in a region of uniform electric field ?? ?? 
along ?? axis. The net electric flux for the entire closed surface is 
(a) ?? ?? ?? 
(b) ???? ?? ?? 
(c) ???? ?? ?? 
(d) zero 
Ans: (d) Explanation: 
Since, field is uniform, the net flux for the closed surface is zero. 
Q2. A block of mass ?? carrying a positive charge ?? is placed on a smooth 
horizontal table, which ends in a vertical wall situated at a distance ?? from 
block. An electric field ?? is switched on towards right. Assuming 
elastic collisions, find the time period of resultant oscillation. 
(a) v
?? ?????? ?? 
(b) v
?????? ????
 
(c) v
?????? ????
 
(d) v
????
????
 
Ans: (b) Acceleration of the block a =
qE
m
 
d =
1
2
at
2
 
Required time = 2?? = v
8md
qE
 
 
 
Q3. Following operations can be performed on a capacitor. 
A: connect the capacitor to a battery of emf E. 
B: Disconnect the battery. 
C: Reconnect the battery with polarity reversed. 
D: Insert a dielectric slab into the capacitor. 
Now choose the incorrect option (s) 
(A) in action ?????? (perform ?? , then ?? and then ?? ), the stored electric energy 
remains unchanged and no thermal energy is developed. 
(B) the charge appearing on capacitor is greater after the action ADB than after 
the action ABD. 
(C) the electric energy stored in the capacitor is greater after the action ?????? 
than the action ?????? . 
(D) the electric field in the capacitor after the action ???? is same as that after the 
action DA. 
Ans:(A) 
Use the concept of capacitor, charging, discharging etc. 
Q4. Gauss's law is frequently written in the following form: 
? ?? ?
. ?? ?? ?
=
?? mec 
?? ?? , 
Where, the symbols have their usual meanings 
(A) this law is true for all closed surfaces 
(B) it is true only in vacuum 
(C) it is true only when the charge distribution is symmetric 
(D) it is true only when the electric field is symmetric 
Ans: (A) 
Gauss's law is true for all closed surface. 
Q5. An electron of mass ?? ?? , initially at rest, moves through a certain distance in 
a uniform electric field in time ?? ?? . A proton of mass ?? ?? , also initially at rest, 
takes time ?? ?? to move through an equal distance in this uniform electric field. 
Neglecting the effect of gravity, the ratio ?? ?? /?? ?? is equal to 
(A) 1 
(B) (
?? ?? ?? ?? )
?? /?? 
(C) (
?? ?? ?? ?? )
?? /?? 
(D) (
?? ?? ?? ?? ) 
Ans. C 
Acceleration in uniform electric field 
a =
qE
m
 
If ?? is time for a distance ?? , 
d =
1
2
(
qE
m
)t
2
 
or, ?? = v
2????
????
 
So, 
t
1
t
2
=
v
m
c
m
p
 
 
 
Q6. If charges ?? /?? and ?? ?? are placed at the centre of face and at the corner of a 
cube, then the total flux through the cube will be 
(A) 
?? ?? ?? ?? 
(B) 
?? ?? ?? 
(C) 
?? ?? ?? ?? 
(D) 
?? ?? ?? ?? 
Ans: A 
Flux through the cube when ?? /2 is placed at the centre of face 
?? 1
=
?? /2
2?? 0
=
?? 4?? 0
 
Flux through the cube when 2?? is placed at the corner of cube is 
?? 2
=
2?? 8?? 0
=
?? 4?? 0
 
Now, total flux through the cube 
?? = ?? 1
+ ?? 2
=
q
2?? 0
 
Q7. A charge +?? is fixed at each of the points ?? = ?? ?? , ?? = ?? ?? ?? , ?? = ?? ?? ?? , … , 8 on the ?? -
axis and a charge -?? is fixed at each of the points ?? = ?? ?? ?? , ?? = ?? ?? ?? , ?? = ?? ?? ?? , … , 8. 
Here, ?? ?? is a positive quantity. Take the electric potential at a point due to 
charge ?? at a distance ?? from it to be 
?? ?? ?? ?? ?? ?? . Then, the potential at origin due to 
the above system of charges is 
(A) 0 
(B) 8 
(C) 
?? ?? ?? ?? ?? ?? ?? ???? ?? 
(D) 
?? ???? ?? ?? ?? ?? ?? ?? ?? 
Ans: D 
V =
q
4?? ?? 0
(
1
x
0
-
1
2x
0
+
1
3x
0
-
1
4x
0
+ ? ) =
q
4?? ?? 0
x
0
(1 -
1
2
+
1
3
-
1
4
+ ? ) =
q
4?? ?? 0
x
0
ln ( 2) 
 
Q8. Find the charge on an iron particle of mass ?? . ???????? , if ?? . ???? % of electrons are 
removed from it. 
(A) -?? . ???????????? 
(B) ?? . ???????????? 
(C) ?? . ?????? 
(D) ?? . ???? 
Ans: B 
 As 
 mass 
 Atomic wt. 
=
 No. of atoms 
 Avogadro No. 
 ? No. of atoms = 24 × 10
18
 atoms 
 = 24 × 10
18
× 26 electrons. 
n = No. of electrons removed = 24 × 10
18
× 26 ×
0.01
100
= 1248
 × 10
14
 electron 
 ? Q = ne = ( + ve charge )= 0.01996C
 
 
Q9. A ring of radius ?? carries a charge +?? . A test charge -?? ?? is released on its 
axis at a distance v?? from its centre. How much kinetic energy will be acquired 
by the test charge when it reaches the centre of the ring? 
(A) 
?? ?? ?? ?? ?? ????
?? 
(B) 
?? ?? ?? ?? ?? (
????
????
) 
(C) 
?? ?? ?? ?? ?? (
????
?? v ?? ?? ) 
(D) 
?? ?? ?? ?? ?? (
????
?? ????
) 
Ans: C 
E
?
= k
q
r
3
r ? 
Electric field due to 10
-9
C at ( 3,1,1) 
E
?
1
= k ×
10
-9
11v11
( 3i ˆ + i ˆ + k
ˆ
) 
Electric field due to Q at ( 3,1,1) 
E
?
2
= k ×
Q
3v3
( i ˆ + i ˆ + k
ˆ
)
E
X
= 0
 
 
 
Q10.  A half ring of radius ?? has a charge of ?? per unit length. The electric field 
at the centre is (?? =
?? ?? ?? ?? ?? ) 
(a) Zero 
(b) 
????
?? 
(c) 
?? ????
?? 
(d) 
??????
?? 
Ans: (c) ???? = ?????? 
Charge on ???? = ???????? . 
Field at ?? due to ???? = ?? ???????? ?? 2
= ???? 
Page 5


Solved Examples on Electrostatics 
JEE Mains 
Q1. The wedge-shaped surface in figure is in a region of uniform electric field ?? ?? 
along ?? axis. The net electric flux for the entire closed surface is 
(a) ?? ?? ?? 
(b) ???? ?? ?? 
(c) ???? ?? ?? 
(d) zero 
Ans: (d) Explanation: 
Since, field is uniform, the net flux for the closed surface is zero. 
Q2. A block of mass ?? carrying a positive charge ?? is placed on a smooth 
horizontal table, which ends in a vertical wall situated at a distance ?? from 
block. An electric field ?? is switched on towards right. Assuming 
elastic collisions, find the time period of resultant oscillation. 
(a) v
?? ?????? ?? 
(b) v
?????? ????
 
(c) v
?????? ????
 
(d) v
????
????
 
Ans: (b) Acceleration of the block a =
qE
m
 
d =
1
2
at
2
 
Required time = 2?? = v
8md
qE
 
 
 
Q3. Following operations can be performed on a capacitor. 
A: connect the capacitor to a battery of emf E. 
B: Disconnect the battery. 
C: Reconnect the battery with polarity reversed. 
D: Insert a dielectric slab into the capacitor. 
Now choose the incorrect option (s) 
(A) in action ?????? (perform ?? , then ?? and then ?? ), the stored electric energy 
remains unchanged and no thermal energy is developed. 
(B) the charge appearing on capacitor is greater after the action ADB than after 
the action ABD. 
(C) the electric energy stored in the capacitor is greater after the action ?????? 
than the action ?????? . 
(D) the electric field in the capacitor after the action ???? is same as that after the 
action DA. 
Ans:(A) 
Use the concept of capacitor, charging, discharging etc. 
Q4. Gauss's law is frequently written in the following form: 
? ?? ?
. ?? ?? ?
=
?? mec 
?? ?? , 
Where, the symbols have their usual meanings 
(A) this law is true for all closed surfaces 
(B) it is true only in vacuum 
(C) it is true only when the charge distribution is symmetric 
(D) it is true only when the electric field is symmetric 
Ans: (A) 
Gauss's law is true for all closed surface. 
Q5. An electron of mass ?? ?? , initially at rest, moves through a certain distance in 
a uniform electric field in time ?? ?? . A proton of mass ?? ?? , also initially at rest, 
takes time ?? ?? to move through an equal distance in this uniform electric field. 
Neglecting the effect of gravity, the ratio ?? ?? /?? ?? is equal to 
(A) 1 
(B) (
?? ?? ?? ?? )
?? /?? 
(C) (
?? ?? ?? ?? )
?? /?? 
(D) (
?? ?? ?? ?? ) 
Ans. C 
Acceleration in uniform electric field 
a =
qE
m
 
If ?? is time for a distance ?? , 
d =
1
2
(
qE
m
)t
2
 
or, ?? = v
2????
????
 
So, 
t
1
t
2
=
v
m
c
m
p
 
 
 
Q6. If charges ?? /?? and ?? ?? are placed at the centre of face and at the corner of a 
cube, then the total flux through the cube will be 
(A) 
?? ?? ?? ?? 
(B) 
?? ?? ?? 
(C) 
?? ?? ?? ?? 
(D) 
?? ?? ?? ?? 
Ans: A 
Flux through the cube when ?? /2 is placed at the centre of face 
?? 1
=
?? /2
2?? 0
=
?? 4?? 0
 
Flux through the cube when 2?? is placed at the corner of cube is 
?? 2
=
2?? 8?? 0
=
?? 4?? 0
 
Now, total flux through the cube 
?? = ?? 1
+ ?? 2
=
q
2?? 0
 
Q7. A charge +?? is fixed at each of the points ?? = ?? ?? , ?? = ?? ?? ?? , ?? = ?? ?? ?? , … , 8 on the ?? -
axis and a charge -?? is fixed at each of the points ?? = ?? ?? ?? , ?? = ?? ?? ?? , ?? = ?? ?? ?? , … , 8. 
Here, ?? ?? is a positive quantity. Take the electric potential at a point due to 
charge ?? at a distance ?? from it to be 
?? ?? ?? ?? ?? ?? . Then, the potential at origin due to 
the above system of charges is 
(A) 0 
(B) 8 
(C) 
?? ?? ?? ?? ?? ?? ?? ???? ?? 
(D) 
?? ???? ?? ?? ?? ?? ?? ?? ?? 
Ans: D 
V =
q
4?? ?? 0
(
1
x
0
-
1
2x
0
+
1
3x
0
-
1
4x
0
+ ? ) =
q
4?? ?? 0
x
0
(1 -
1
2
+
1
3
-
1
4
+ ? ) =
q
4?? ?? 0
x
0
ln ( 2) 
 
Q8. Find the charge on an iron particle of mass ?? . ???????? , if ?? . ???? % of electrons are 
removed from it. 
(A) -?? . ???????????? 
(B) ?? . ???????????? 
(C) ?? . ?????? 
(D) ?? . ???? 
Ans: B 
 As 
 mass 
 Atomic wt. 
=
 No. of atoms 
 Avogadro No. 
 ? No. of atoms = 24 × 10
18
 atoms 
 = 24 × 10
18
× 26 electrons. 
n = No. of electrons removed = 24 × 10
18
× 26 ×
0.01
100
= 1248
 × 10
14
 electron 
 ? Q = ne = ( + ve charge )= 0.01996C
 
 
Q9. A ring of radius ?? carries a charge +?? . A test charge -?? ?? is released on its 
axis at a distance v?? from its centre. How much kinetic energy will be acquired 
by the test charge when it reaches the centre of the ring? 
(A) 
?? ?? ?? ?? ?? ????
?? 
(B) 
?? ?? ?? ?? ?? (
????
????
) 
(C) 
?? ?? ?? ?? ?? (
????
?? v ?? ?? ) 
(D) 
?? ?? ?? ?? ?? (
????
?? ????
) 
Ans: C 
E
?
= k
q
r
3
r ? 
Electric field due to 10
-9
C at ( 3,1,1) 
E
?
1
= k ×
10
-9
11v11
( 3i ˆ + i ˆ + k
ˆ
) 
Electric field due to Q at ( 3,1,1) 
E
?
2
= k ×
Q
3v3
( i ˆ + i ˆ + k
ˆ
)
E
X
= 0
 
 
 
Q10.  A half ring of radius ?? has a charge of ?? per unit length. The electric field 
at the centre is (?? =
?? ?? ?? ?? ?? ) 
(a) Zero 
(b) 
????
?? 
(c) 
?? ????
?? 
(d) 
??????
?? 
Ans: (c) ???? = ?????? 
Charge on ???? = ???????? . 
Field at ?? due to ???? = ?? ???????? ?? 2
= ???? 
We need to consider only the component ???? cos ?? , as the component ???? sin ?? will cancel out 
because of the field at ?? due to the symmetrical element ???? ', 
The total field at ?? is = 2?
0
?? /2
????? cos ?? = 2
????
?? ?
0
?? /2
?cos ?????? = 2?? ?? ?? {=
?? 2?? ?? 0
?? 2
} 
 
Q11. Two point charges ?? and -?? ?? are placed at some distance apart. If the 
electric field at the location of ?? is ?? , then at the locality of - ?? ?? , it is 
(a) -?? 
(b) ?? /?? 
(c) -?? ?? 
(d) -?? /?? 
Ans: (b) Let the charge ?? and -3?? be placed respectively at ?? and ?? at a distance ?? 
Now we will determine the magnitude and direction to the field produced by charge -3?? at 
A, this is ?? as mentioned in the Example. 
? ?? =
3?? ?? 2
 (along AB directed towards negative charge) 
Now field at location of - 3?? i.e. field at ?? due to charge ?? will be ?? '
=
?? ?? 2
=
?? 3
 (along ???? 
directed away from positive charge) 
Q12. The number of electrons to be put on a spherical conductor of radius ?? . ?? ?? 
to produce an electric field of ?? . ?????? ?? /?? just above its surface is 
(a) ?? . ?? × ????
?? 
(b) ?? . ?? × ????
?? 
(c) ?? . ?? × ????
?? 
(d) ?? . ?? × ????
?? 
Ans: (c) By using ?? = ?? ?? ?? 2
, where ?? = radius of sphere so 0.036 = 9 × 10
9
×
????
( 0.1)
2
? ?? =
2.5 × 10
5
 
Example: 30 Infinite charges are lying at ?? = 1,2,4,8 … meter on ?? -axis and the value of each 
charge is ?? . The value of intensity of electric field and potential at point ?? = 0 due to these 
charges will be respectively 
(a) 12 × 10
9
?? N/C, 1.8 × 10
4
 V 
(b) 
(c) 6 × 10
9
QN/C, 9 × 10
3
 V V 
 Zero, 1.2 × 1O
4
 V
4 × 10
9
Q N/C, 6 × 1O
3
 
Solution: (a) By the superposition, Net electric field at origin 
?? = ???? [
1
1
2
+
1
2
2
+
1
4
2
+
1
8
2
+ ? 8]
?? = ???? [1 +
1
4
+
1
16
+
1
64
+ ? 8]
 
1 +
1
4
+
1
16
+
1
64
+ ? 8 is an infinite geometrical progression it's sum can be obtained by using 
the formula ?? 8
=
?? 1-?? ; Where ?? = First term, ?? = Common ratio.