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JEE Main 26-Aug-2021 Shift 2 Solved Paper
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© examsnet.com
Question : 7
Total: 90
The two thin co-axial rings, each of radius a and having charges +Q and -Q respectively, are separated by a distance of s. The potential difference between the centres of the two rings is
[26 Aug 2021 Shift 2]
Q
2
π
ε
0
[
1
a
+
1
√
s
2
+
a
2
]
Q
4
π
ε
0
[
1
a
+
1
√
s
2
+
a
2
]
Q
4
π
ε
0
[
1
a
−
1
√
s
2
+
a
2
]
Q
2
π
ε
0
[
1
a
−
1
√
s
2
+
a
2
]
Validate
Solution:
Given, charges on two rings are +Q and -Q, respectively as shown below.
Potential at centre of ring A due to charge on ring A and charge onring B is given as
V
A
=
k
Q
a
−
k
Q
√
s
2
+
a
2
Similarly, potential at centre of ring B due to charge on ring B and charge on ring A is given as
V
B
=
−
k
Q
a
+
k
Q
√
s
2
+
a
2
Potential difference between centre of both the rings is
Δ
V
=
V
A
−
V
B
=
k
Q
a
−
k
Q
√
s
2
+
a
2
−
(
−
k
Q
a
+
k
Q
√
s
2
+
a
2
)
=
2
k
Q
a
−
2
k
Q
√
s
2
+
a
2
=
Q
2
π
ε
0
(
1
a
−
1
√
s
2
+
a
2
)
(
∵
k
=
1
4
π
ε
0
Nm
2
C
−
2
)
Thus, potential difference between centre of both the rings is
Q
2
π
ε
0
[
1
a
−
1
√
s
2
+
a
2
]
© examsnet.com
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