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Q.

A current i ampere flows in a circular arc of wire whose radius is R, which subtend an angle 3 $π$ /2 radian at its centre. The magnetic induction B at the centre is

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a

$\frac{μ_{0} i}{R}$

b

$\frac{μ_{0} i}{2 R}$

c

$\frac{2 μ_{0} i}{R}$

d

$\frac{3 μ_{0} i}{8 R}$

answer is D.

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Detailed Solution

Magnetic field induction at O is

Question Image

$B = \frac{3}{4} (d u e t o w h o l e c i r c l e) = \frac{3}{4} (\frac{μ_{0} i}{2 R}) = \frac{3 μ_{0} i}{8 R}$

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A current i ampere flows in a circular arc of wire whose radius is R, which subtend an angle 3π/2 radian at its centre. The magnetic induction B at the centre is