Question

A particle carrying charge equal to $100$ times the charge of an electron is performing one rotation per second in a circular path of radius $0.8\text{m}$. The value of magnetic field produced at the centre will be
( ${\mu }_0=$ permeability for vaccum )

• A. $\frac{{10}^{-7}}{{\mu }_0}\text{T}$
• B. ${10}^{-17}{\mu }_0\text{T}$
• C. ${10}^{-6}{\mu }_0\text{T}$
• D. ${10}^{-16}{\mu }_0\text{T}$

Answer 1

The correct option is B ${10}^{-17}{\mu }_0\text{T}$

As the charge is performing one rotation per second, so comparing this with an equivalent current in a circular wire,

$i=\frac{q}{t}=\frac{100\times e}{1}$

$i=100\times 1.6\times {10}^{-19}\text{A}$

Now the magnetic field due to the loop at the centre is,

$B=\frac{{\mu }_{0}i}{2R}=\frac{{\mu }_0\times 100\times 1.6\times {10}^{-19}}{2\times 0.8}$

$={10}^{-17}{\mu }_0\text{T}$

Hence, option $\left(b\right)$ is correct.