Question

A solenoid of length 0.4 m, having 500 turns and 3A current flows through it. A coil of radius 0.01 m and have 10 turns and carries current of 0.4 A has to placed such that its axis is perpendicular to the axis of solenoid ,then torque on coil will be

• A. $5.92\times {10}^{-7}N.m$
• B. $5.92\times {10}^{-5}N.m$
• C. $5.92\times {10}^{-4}N.m$
• D. $5.92\times {10}^{-3}N.m$

Answer 1

The correct option is A $5.92\times {10}^{-7}N.m$

Magnetic field due to larges solenoid

$B=\frac{{\mu }_{0}NI}{l}=\frac{4\times {10}^{-7}\times 500\times 3}{0.4}$

$N=500$

$I=3$

$l=0.4$

Torque $M$ solenoid $I\times$ Area of corn section $\times B$

$=0.4\times \pi {0.01}^2\times 4\pi \times \frac{{10}^{-7}\times 500\times 3}{0.4}$

orque $=\pi .0{.01}^2\times 4\pi \times {10}^{-7}\times 500\times 3$

Torque $=5.92\times {10}^{-7}N-m$