Question

Three identical long solenoids $\text{P, Q}$ and $\text{R}$ having equal resistance $r$ are connected to each- other as shown in figure. If the magnetic field at the centre of $\text{P}$ is $2B$, what would be the field at the centre of $\text{Q}$ ?

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

Answer 1

The correct option is A $B$

As the solenoids are identical and having equal resistance $r$, the currents in $\text{Q}$ and $\text{R}$ will be same and will be half of the current in $\text{P}$.

$\therefore i_Q=i_R=i_P/2$

Magnetic field due to the long solenoid is given by

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

$B\propto i\text{(for identical solenoid)}$

$\therefore \frac{B_Q}{B_P}=\frac{i_Q}{i_P}=\frac{i_P/2}{i_P}=\frac{1}{2}$

$\therefore B_Q=\frac{B_P}{2}=\frac{2B}{2}=B$

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

Why this question ? Tip : This question gives the relation between resistance and magnetic field.