Question

As shown in the figure, a long straight conductor with semicircular are of radius $\frac{\pi}{10} m$ is carrying current $I =3 A$. The magnitude of the magnetic field. at the center $O$ of the arc is :
(The permeability of the vacuum $=4 \pi \times 10^{-7}\, NA ^{-2}$ )

• A. $6\, \mu T$
• B. $4 \,\mu T$
• C. $3\, \mu T$
• D. $1\, \mu T$

Answer 1

Answer: (C)

$B _{ C } =\frac{\mu_0 I }{4 \pi R }(\pi)( B \text { at centre of circular arc })$
$=\frac{\mu_0 I }{4 R }=\frac{4 \pi \times 10^{-7} \times 3}{4 \times \frac{\pi}{10}} $
$ =3 \times 10^{-6} T =3 \mu T$