Question

A current of $0.1A$ circulates around a coil of $100$ turns and having a radius equal to $5cm$. The magnetic field set up at the center of the coil is : $\left({\mu }_0\right)=4\pi \times {10}^{-7}\text{Wb/A - m})$

• A. $4\pi \times {10}^{-5}T$
• B. $8\pi \times {10}^{-5}T$
• C. $4\times {10}^{-5}T$
• D. $2\times {10}^{-5}T$

Answer 1

The correct option is A $4\pi \times {10}^{-5}T$

Given:

The current circulating in the coil is $I=0.1A$.

The number of turns in the coil is $N=100turns$

The radius of the coil is $r=5cm$

The magnetic field at the center of coil is:

$B=\frac{{\mu }_0}{4\pi }.\frac{{\mu }_{0}Ni}{2r}$

$=\frac{2\pi \times {10}^{-7}\times 100\times 0.1}{5\times {10}^{-2}}$

$=4\pi \times {10}^{-5}Tesla$