Question

A long straight wire of radius R carries current $i$. The magnetic field inside the wire at distance r from its centre is expresses as:

• A. $\left(\frac{{\mu }_{0}i}{\pi R^2}\right).r$
• B. $\left(\frac{2{\mu }_{0}i}{\pi R^2}\right).r$
• C. $\left(\frac{{\mu }_{0}i}{2\pi R^2}\right).r$
• D. $\left(\frac{{\mu }_{0}i}{2\pi R}\right).r$

Answer 1

The correct option is C $\left(\frac{{\mu }_{0}i}{2\pi R^2}\right).r$

Using Ampere's law, we have $\varphi \underset{B}{\to }.\underset{dl}{\to }={\mu }_0{i}_{in}$
or $B\times 2\pi r={\mu }_0\frac{I{r}^2}{R^2}(\because J=\frac{I}{A}=\frac{I}{.\pi r^2})$ Current enclosed inside the radius r. So$I=\frac{i{r}^2}{R^2}$
$\therefore B=\frac{{\mu }_0}{2\pi }.\frac{ir}{R^2}$