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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 R√3 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)32⇒2=(1+x2R2)12 ⇒ 4=1+x2R2⇒3=x2R2⇒x2=3R2⇒x=√3R

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