A current i ampere flows in a circular arc of wire whose radius i… - Vidyadip

MCQ

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

A
$\frac{{{\mu _0}i}}{R}$
B
$\frac{{{\mu _0}i}}{{2R}}$
C
$\frac{{2{\mu _0}i}}{R}$
✓
$\frac{{3{\mu _0}i}}{{8R}}$

✓

Answer

Correct option: D.

$\frac{{3{\mu _0}i}}{{8R}}$

d
(d) $B = \frac{{{\mu _0}}}{{4\pi }}\frac{{(2\pi - \theta )i}}{R} = \frac{{{\mu _0}}}{{4\pi }}\frac{{\left( {2\pi - \frac{\pi }{2}} \right) \times i}}{R}$$ = \frac{{3{\mu _0}i}}{{8R}}$

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