Question

The magnetic field at the centre of semi-circular wire carrying current $ i $ is

• A. $ \frac{{{\mu }_{0}}i}{2r} $
• B. $ \frac{{{\mu }_{0}}i}{4r} $
• C. $ \frac{{{\mu }_{0}}i}{r} $
• D. $ \frac{{{\mu }_{0}}i}{2\pi r} $

Answer 1

Answer: (B)

Magnetic field at centre of a circular coil,
$B=\frac{\mu_{0} N i}{2 r}$
Here $N=\frac{1}{2}$
$\therefore B =\frac{\mu_{0}\left(\frac{1}{2}\right) i}{2 r}$
$=\frac{\mu_{0} i}{4 r}$