Question

The magnetic field insides a toroid of radius $r$ is $B$. If the radius of toroid is quadrupled and number of turns is increased by $8$ times keeping the current constant. Find the new magnetic field inside the core of toroid.

• A. $B$
• B. $\frac{B}{2}$
• C. $2B$
• D. $4B$

Answer 1

The correct option is C $2B$

Magnetic field produced by toroid inside the core of toroid is given by

$B=\frac{{\mu }_{0}Ni}{2\pi r}.....\left(1\right)$

In question given that
$r^{\prime }=4r;i^{\prime }=i$ and $N^{\prime }=8N$

$\therefore B^{\prime }=\frac{{\mu }_0{N}^{\prime }i}{2\pi r^{\prime }}=\frac{{\mu }_0\left(8N\right)i}{2\pi \left(4r\right)}=2\times \frac{{\mu }_{0}Ni}{2\pi r}$

From equation $\left(1\right)$, we get

$B^{\prime }=2B$

So, option $\left(c\right)$ is correct.