Question

Hollow cylindrical wire carries current $I$ , having inner and outer radii $R$ and $2R$ respectively. The magnetic field at a point which is $\frac{5 R}{4}$ distance away from the wire:-

• A. $\frac{5 \mu _{0} I}{18 \pi R}$
• B. $\frac{\mu _{0} I}{36 \pi R}$
• C. $\frac{5 \mu _{0} I}{36 \pi R}$
• D. $\frac{3}{40}\frac{\mu _{0} I}{\pi R}$

Answer 1

Answer: (D)

$i_{\text{in }}=\frac{I\pi \left(\frac{25 R^{2}}{16} - R^{2}\right)}{3 \pi R^{2}}$
$i_{\text{in }}=\frac{3 I}{16}$
$B=\frac{\mu_0 i_{i n}}{2 \pi\left(\frac{5 R}{4}\right)} \quad \Rightarrow \quad B=\frac{\mu_0(3 I / 16)}{5 \pi R / 2}=\frac{3 \mu_0 I}{40 \pi R}$