First slide

Magnetic field due to a current carrying circular ring

Question

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

Moderate

A

$\frac{μ_{0} i}{R}$
B

$\frac{μ_{0} i}{2 R}$
C

$\frac{2 μ_{0} i}{R}$
D

$\frac{3 μ_{0} i}{8 R}$

Solution

$B = \frac{μ_{0}}{4 π} \frac{(2 π - θ) i}{R} = \frac{μ_{0}}{4 π} \frac{(2 π - \frac{π}{2}) \times i}{R} = \frac{3 μ_{0} i}{8 R}$

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