Question

A solenoid $1.0\text{m}$ long and $0.05\text{m}$ diameter has $700$ turns. Another solenoid of 50 turns is tightly wound over the first solenoid. Find the emf induced in the second solenoid when the current in the first solenoid changes from $0$ to $5\text{A}$ in $0.01\text{s}$.

• A. $4.3\times {10}^{-2}\text{V}$
• B. $2.1\times {10}^{-2}\text{V}$
• C. $4.3\times {10}^{-3}\text{V}$
• D. $2.1\times {10}^{-3}\text{V}$

Answer 1

The correct option is A $4.3\times {10}^{-2}\text{V}$

Mutual inductance $M=\frac{{\mu }_{0}A{N}_1{N}_2}{l}$
$=\frac{4\pi \times {10}^{-7}\times \pi (0.025{)}^2\times 700\times 50}{1.0}$
$=8.6\times {10}^{-5}\text{H}$
$|e|=M\frac{dl}{dt}=8.6\times {10}^{-5}\times \frac{5-0}{0.01}=4.3\times {10}^{-2}\text{V}$