Question

A current of $10A$ is passing through a long wire which has semicircular loop of the radius $20cm$ 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,
$I=10A$,
$r=20cm$
$=20\times 10^{-2}m$
$=\frac{1}{2}\times \frac{4\pi \times 10^{-7}\times 10}{2\times 20\times 10^{-2}}$
$=\frac{\pi \times 10^{-6}}{20\times 10^{-2}}=5\pi \times 10^{-6}T$
$=5\pi \mu T$