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Question

# A point charge Q is located at centre of a fixed thin ring of radius R with uniformly distributed charge −Q. The magnitude of the electric field strength at the point lying on the axis of the ring at a distance x from the centre is (x>>R)

A
QR28πε0x4
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B
3QR28πε0x4
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C
5QR28πε0x4
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D
7QR28πε0x4
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Solution

## The correct option is B 3QR28πε0x4Electric field at point P due to +Q is∈1KQx2→(i)Electric point at point P due to ring is∈2=−KQx(x2+R2)32→(ii)Net electric field at P is ∈=∈1+∈2∴KQx2+−KQx(x2+R2)32⇒∈=KQx2+−KQxx3(1+R2x2)32⇒∈=KQx2⎡⎢⎣1−(1+R2x2)−32⎤⎥⎦→(iii)sinex≫R,R2x2≪1,usingbinomialsweget∈=KQx2[12−{1+(−32)(R2x2)}]e∈=KQx2[1−1+3R22x2]∈=3QR28π∈⋅x4(K=14π∈o)

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