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Question

# Along the X-axis, three chargesq2,−q and q2 are placed at x = 0, x = a and x = 2a respectively. The resultant electric potential at x = a+r (if, a << r) is :( ϵ0 is the permittivity of free space)

A
qa4πϵ0r2
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B
qa24πϵ0r3
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C
q(a2/4)4πϵ0r3
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D
q4πϵ0r
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Solution

## The correct option is A qa24πϵ0r3Electric potentialV=14πϵoqr=kqrpotential at (a+r) is the sum of the potentials of all three charges at that pointVR=kq2(a+r−0)−kqa+r−a+kq2((a+r)−2a)VR=kq(r(r−a)−2(r−a)(a+r)+r(a+r)2(a+r)(r−a)r)=kqa2r3−a2ras the assumption is a<<r we can neglect aV=kqa2r3=14πϵoqa2r3

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