Question

For a given solenoid, a constant current of $0.2\text{A}$ is flowing, initially there were $500$ turns for $0.5\text{m}$ length of solenoid. What will be the ratio of magnetic field at the centre of solenoid if the number of turns is increased to $2000$ and length $1.5\text{m}$ keeping the current constant.

• A. $1:2$
• B. $2:3$
• C. $4:3$
• D. $3:4$

Answer 1

The correct option is D $3:4$

We know that,

$B={\mu }_{0}ni$

$B\propto n(\because {\mu }_0\&i\text{are constant})$

$\therefore \frac{B_1}{B_2}=\frac{n_1}{n_2}=\frac{N_1/l_1}{N_2/l_2}$

Here,
$N_1=500;l_1=0.5\text{m}$
$N_2=2000;l_2=1.5\text{m}$

$\frac{B_1}{B_2}=\frac{500/0.5}{2000/1.5}=\frac{500}{0.5}\times \frac{1.5}{2000}$

$\therefore \frac{B_1}{B_2}=\frac{3}{4}=3:4$

Therefore, $\left(d\right)$ is the right option.