Question

The magnetic field inside a toroid of radius $R$ is $B$. If the current through it is doubled and the radius increased four times keeping the number of turns per unit length same, then the magnetic field produced by it will be

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

Answer 1

The correct option is B $2B$

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

$B=\frac{{\mu }_{0}Ni}{2\pi r}={\mu }_{0}ni$

Where, $n=\frac{N}{2\pi r}=$ number of tunrs per unit length

$\therefore B\propto i\text{(for same}n)$

So, $\frac{B_2}{B_1}=\frac{i_2}{i_1}$

From question, $B_1=B;i_2=2i_1$

$\therefore B_2=2B$

$\therefore$ New magnetic field, $B_1=2B$

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

Why this question ? Caution: In this question $n$ is constant but $N$ is not. Here change in the radius is given to create confusion in the student's mind.