Question

A circular loop of radius $R$ carries a current of $5\text{A}$. If the magnetic field $B$ at the centre is $0.02\text{mT}$. The magnetic field at the centre of the loop if the radius of it is increased by $\frac{\pi }{2}\text{m}$ keeping current same is

• A. $0.01\text{mT}$
• B. $0.02\text{mT}$
• C. $0.03\text{mT}$
• D. $0.04\text{mT}$

Answer 1

The correct option is A $0.01\text{mT}$


Magnetic field at the centre of circular current carrying loop is given by,

$B=\frac{{\mu }_{0}I}{2R}$

Initially,
$B=0.02\text{mT}=0.02\times {10}^{-3}\text{T}$ and $I=5\text{A}$


$\Rightarrow R=\frac{{\mu }_{0}I}{2B}=\frac{2\pi \times {10}^{-7}\times 5}{0.02\times {10}^{-3}}=\frac{\pi }{2}\text{m}$

According to problem, new radius

$R_{new}=R+\frac{\pi }{2}=\frac{\pi }{2}+\frac{\pi }{2}=\pi$

$\Rightarrow R_{new}=2R$

As, $B\propto \frac{1}{R}[\because I=\text{constant}]$

So, the new magnetic field,

$B_{new}=\frac{B}{2}=\frac{0.02}{2}=0.01\text{mT}$

Hence, option (a) is the correct answer.