Question

A thin straight conductor lies along the axis of a hollow conductor of radius $R=0.2\text{m}$, both of them carries $2\text{A}$ current in the same direction. Find magnetic induction at a distance $R$ from the axis of the hollow cylinder.

• A. $20\times {10}^{-7}\text{T}$
• B. $10\times {10}^{-7}\text{T}$
• C. $30\times {10}^{-7}\text{T}$
• D. $40\times {10}^{-7}\text{T}$

Answer 1

The correct option is D $40\times {10}^{-7}\text{T}$

Given:
$R=0.2\text{m};i=2\text{A}$

Using Ampere's law for magnetic induction at point $\text{P}$ is,

$\oint \overrightarrow{B}\cdot \overrightarrow{dl}={\mu }_0{i}_{net}$

Here, $i_{net}=4\text{A}$ and $\oint dl=2\pi R$

$\therefore B\left(2\pi R\right)={\mu }_0\left(2i\right)$

$B=\frac{4\pi \times {10}^{-7}\times 2\left(2\right)}{2\pi \times \left(0.2\right)}$

$\therefore B=40\times {10}^{-7}\text{T}$

Hence, option $\left(d\right)$ is the right choice.