A small loop of area 3.1 m`m^(2)` is placed inside a long solenoid that has 672 turns/cm and carries a sinusoidally varying current i of amplitude 1.28 A and angular frequency 212 rad/s. The central axes of the loop and solenoid coincide. What is the amplitude of the emf induced in the loop?

Explanation

To solve the problem of finding the amplitude of the emf induced in a small loop placed inside a long solenoid, we can follow these steps:

### Step 1: Identify the given values
- Area of the loop, \( A = 3.1 \, \text{mm}^2 = 3.1 \times 10^{-6} \, \text{m}^2 \)
- Number of turns per unit length of the solenoid, \( n = 672 \, \text{turns/cm} = 67200 \, \text{turns/m} \)
- Amplitude of current, \( I_0 = 1.28 \, \text{A} \)
- Angular frequency, \( \omega = 212 \, \text{rad/s} \)

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