Question

Two coaxial solenoids of different radii carry current $I$ in the same direction. Let ${\overrightarrow{F}}_1$ be the magnetic force on the inner solenoid due to the outer one and ${\overrightarrow{F}}_2$ be the magnetic force on the outer solenoid due to the inner one. Then

• A. $\overrightarrow{F_1}$ is radially inwards and $\overrightarrow{F_2}=0$
• B. $\overrightarrow{F_1}$ is radially outwards and $\overrightarrow{F_2}=0$
• C. $\overrightarrow{F_1}=\overrightarrow{F_2}=0$
• D. $\overrightarrow{F_1}$ is radially inwards and $\overrightarrow{F_2}$ is radially outwards

Answer 1

The correct option is C $\overrightarrow{F_1}=\overrightarrow{F_2}=0$

$\text{Given:-}$ Two coaxial solenoids of different radii carry

current $I$ in the same direction.

The magnetic force on the inner solenoid due to the outer one = $F_1$

The magnetic force on the outer solenoid due to the inner one = $F_2$

$\text{Solution:-}$ Consider the two coaxial solenoids, Due to one of the solenoids magnetic field at the center of the other can be assumed to be constant.

Due to symmetry, forces on the upper and lower part of a solenoid will be equal and opposite and hence resultant is zero.

Therefore, $F_1=F_2$

$\text{Hence the correct option is C}$