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Question

A circular current carrying coil has a radius R. The distance from the centre of the coil on the axis where the magnetic induction will be 18th to its value at the centre of the coil, is

A
R3
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B
R3
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C
23R
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D
23R
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Solution

The correct option is B R3

The field on the axis of a current carrying at distance "x" from centre is given by
B=μ0NiR22(R2+x2)32
At centre, x = 0
Bcentre=μ0Ni2R
BcentreBaxis=(1+x2R2)32
also Baxis=18Bcentre
81=(1+x2R2)322=(1+x2R2)12
4=1+x2R23=x2R2x2=3R2x=3R

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