Question

Assume a long solenoid is wound with $500$ turns $m^{-1}$ and current is increasing at $100A{s}^{-1}$. The cross-section of the coil has an area of $4c{m}^2$. Find the induced electric field within the loop of radius $2cm$.

• A. $2\times {10}^{-4}V{m}^{-1}$
• B. $4\times {10}^{-4}V{m}^{-1}$
• C. $3\times {10}^{-4}V{m}^{-1}$
• D. none of these

Answer 1

The correct option is A $2\times {10}^{-4}V{m}^{-1}$

$\epsilon =-{\mu }_{0}nA\frac{dI}{dt}$
$=4\pi \times {10}^{-7}\times 500\times 4\times {10}^{-4}\times 100=8\pi \times {10}^{-6}V$
$\oint E.dl=\epsilon orE=\frac{\epsilon }{2\pi r}$
$=\frac{8\pi \times {10}^{-6}}{2\pi \times 2\times {10}^{-2}}=2\times {10}^{-4}V$