Question

Shown in the figure is a conductor carrying a current $I.$ The magnetic field intensity at the point $O$ (common centre of all the three arcs) is :-

• A. $\frac{5 \mu _{0} I\theta }{24 \pi r}$
• B. $\frac{\mu _{0} I\theta }{24 \pi r}$
• C. $\frac{11 \mu _{0} I\theta }{24 \pi r}$
• D. zero

Answer 1

Answer: (A)

since, magnetic field at the centre of an arc is equal to
$B=\frac{\mu _{o} I}{4 \pi r}\theta $
Hence, net $B=\frac{\mu _{0} I}{4 \pi }\left[\frac{1}{r} - \frac{1}{2 r} + \frac{1}{3 r}\right]\theta $
$=\frac{5 \mu _{0} I\theta }{24 \pi r}$