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Byju's Answer
Standard XII
Physics
Gravitation vs. Electrostatics
Four point ch...
Question
Four point charges Q, q, Q and q are placed at the corners of a square of side 'a' as shown in the figure. Q q
Find the
(a) resultant electric force on a charge Q and
(b) potential energy of this system.
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Solution
(a) Force on charge Q at B due to charge q
F
2
=
1
4
π
ϵ
0
q
Q
a
2
along
→
B
Y
F
2
=
1
4
π
ϵ
0
q
Q
a
2
along
→
B
X
Resultant force,
F
=
√
F
2
1
+
F
2
2
along
→
B
O
=
√
2
(
1
4
π
ϵ
0
q
Q
a
2
)
2
=
q
Q
√
2
4
π
ϵ
0
a
2
Force due to charge
Q
=
F
3
=
1
4
π
ϵ
0
Q
Q
(
√
2
a
2
)
along
→
B
O
Total resultant force =
F
+
F
3
along
→
B
O
=
1
4
π
ϵ
0
√
2
Q
q
a
2
+
1
4
π
ϵ
0
Q
Q
2
a
2
=
[
1
4
π
ϵ
0
Q
a
2
(
√
2
q
+
Q
2
)
]
along
→
B
O
(b) Total potential energy of the system,
U
=
1
4
π
ϵ
0
[
Q
q
a
+
Q
q
a
+
Q
q
a
+
Q
q
a
+
Q
q
a
+
Q
Q
√
2
a
+
q
q
√
2
a
]
=
1
4
π
ϵ
0
[
4
Q
q
a
+
Q
2
√
2
a
+
q
2
√
2
a
]
=
1
4
π
ϵ
0
[
4
Q
q
+
Q
2
+
q
2
√
2
]
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