Question

Two wires are bent (shown as joint-circle) with radius $r$ (in $xy$ plane). The upper half has resistance of $2R\Omega$ and the lower half of $R\Omega$ . A current $I$ is passed into circle as shown. The magnetic field at centre is :

• A. $\frac{\left(\mu \right)_{0} I}{r}\left(\hat{k}\right)$
• B. $\frac{\left(\mu \right)_{0} I}{2 r}\left(\hat{k}\right)$
• C. zero
• D. $\frac{\left(\mu \right)_{0} I}{12 r}\left(\hat{k}\right)$

Answer 1

Answer: (D)

Magnetic field at centre,
$B_{C}=\frac{\left(\mu \right)_{0}}{4 r}\left[\left(\frac{2 I}{3}\right) - \left(\frac{I}{3}\right)\right]=\frac{\left(\mu \right)_{0} I}{12 r}$
outward so direction is along $\hat{k}$ .