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Question

Two equal positive charges are kept at points A and B. The electric potential at the points between A and B (excluding the points A and B) is studied while moving from A to B. Then the electric potential will

A
continously increase
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B
continously decrease
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C
first increase and then decrease
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D
first decrease and then increase
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Solution

The correct option is D first decrease and then increase
Suppose the charges are + q and kept at r0 distance apart.


Now, let us take a point at distance x from A.
The net electric potential at point P,
VP = kqx + kqr0x
VP= kqr0kqx+kqxx(r0x)
Or, VP= kqr0x(r0x) ....(i)
At point C,
x= r04
C is taken as the midpoint of AO
VC = 16kq3r0 = 5.3 × kqr0

Similarly at point O,
x= r02
AO is taken as the mid-point of AB,
VO = 4kqr0
(from Eq.(i))
VO= 4 × kqr0

At point D,
x=AD = 34r0
VD = 16kq3r0 = 5.3 × kqr0

From above observations of potential at points C, O, D we can see that while moving from A to B, the electric potential first decreases and then increases.
Therefore, option(d) is correct choice.


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