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Question

A wire having a uniform linear charge density λ is bent in the form of a ring of radius R. Point A as shown in the figure, is in the plane of the ring but not at the centre. Two elements of the ring of lengths, a1 and a2 subtend very small and equal angles at point A. They are at distances, r1 and r2 from point A respectively. Then -

A
The ratio of charge on elements a1 and a2 is r1r2.
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B
The element a1 produces a greater magnitude of electric field at A than element a2.
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C
The elements a1 and a2 produce same potential at A.
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D
The elements a1 produces greater potential at A than element a2.
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Solution

The correct option is C The elements a1 and a2 produce same potential at A.


Charge on a1 is r1θλ
[ Assuming small angle subtended by elements at A to be θ]

Similarly, charge on a2 is r2θλ

So, ratio of charges is r1r2.

Now, electric field produced by a1 at A,
E1=kr1θλr21=kθλr1

Similarly, by a2,
E2=kθλr2

As r2>r1E1>E2

Further, electric potential by a1 at A,
V1=kr1θλr1=kθλ

Similarly, by a2,
V2=kr2θλr2=kθλ

V1=V2

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