Question

A current of $ 10 \,A $ is passing through a long wire which has semicircular loop of the radius $ 20 \,cm $ as shown in the figure. Magnetic field produced at the centre of the loop is

• A. $ 10\pi\,\mu T $
• B. $ 5\pi\,\mu T $
• C. $ 4\pi\,\mu T $
• D. $ 2\pi\,\mu T $

Answer 1

Answer: (B)

Magnetic field produced at the centre
$B=\frac{1}{2} \left(\frac{\mu_{0}I}{2r}\right)$
According to question,
$I=10\,A$,
$r=20\,cm$
$=20\times10^{-2}\,m$
$=\frac{1}{2}\times\frac{4\pi\times10^{-7}\times10}{2\times20\times10^{-2}}$
$=\frac{\pi\times10^{-6}}{20\times10^{-2}}=5\pi\times10^{-6}T $
$=5\pi\,\mu T$