Question

A long straight wire of radius $R$ carries a current $i$ . The magnetic field inside the wire at distance $r\left(\right.r < R\left.\right)$ , from its centre is expressed as

• A. $\left(\frac{\mu_0 i}{\pi R^2}\right) \cdot r$
• B. $\left(\frac{2 \mu_0 i}{\pi R^2}\right) \cdot r$
• C. $\left(\frac{\mu_0 i}{2 \pi R^2}\right) \cdot r$
• D. $\left(\frac{\mu_0 i}{2 \pi R}\right) \cdot r$

Answer 1

Answer: (C)

Using Ampere's law, we have
$\oint \overset{ \rightarrow }{B}.\overset{ \rightarrow }{d l}=\mu _{0} \, i_{i n}$

or $B\times 2\pi r=\mu _{0}\frac{i}{\pi R^{2}}\pi r^{2}$
$\therefore $ $B=\frac{\mu _{0}}{2 \pi }.\frac{i r}{R^{2}}$