JEE Main · PhysicsHard
A solenoid of length $l$, radius $r$, and $n$ turns per unit length carries a current $I = I_0 \cos(\omega t)$. The induced electric field at a distance $r/2$ from the axis inside the solenoid is?
- A.$\frac{\mu_0 n I_0 \omega r \sin(\omega t)}{4}$
- B.$\frac{\mu_0 n I_0 \omega r \sin(\omega t)}{2}$
- C.$\frac{\mu_0 n I_0 \omega r \cos(\omega t)}{4}$
- D.$\frac{\mu_0 n I_0 \omega r \sin(\omega t)}{8}$
Show correct answer & step-by-step solution
Correct answer: A — $\frac{\mu_0 n I_0 \omega r \sin(\omega t)}{4}$
Solution
Using Faraday's law in integral form, . The magnetic field is , and the flux is , leading to .
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