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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 3QR28πε0x4
Electric 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+2KQx2+KQx(x2+R2)32=KQx2+KQxx3(1+R2x2)32=KQx21(1+R2x2)32(iii)sinexR,R2x21,usingbinomialsweget=KQx2[12{1+(32)(R2x2)}]e=KQx2[11+3R22x2]=3QR28πx4(K=14πo)

1215012_1117063_ans_f2465ab301254e37afc1d663105db1b8.PNG

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