Question

A small loop of area 8.8 mm² is placed inside a long solenoid that has 818 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?

Answer 1

The amplitude of the induced emf is
`\epsilon_a = 2.45*10^(-4)\ V`

Step-by-step explanation:

From the question we are told that

The area is
`A = 8.8 \ mm^2 = 8.8 *10^(-6) \ m`

The number f turns per cm is
`N = 818 \ turn/cm = 81800 \ turn /m`

The current is
`I = 1.28 \ A`

The angular frequency is
`w = 212 \ rad /s`

Generally the amplitude of the induced emf is mathematically represented as

`\epsilon_a = \mu_o * N * I * w * A`

Where
`\mu_o` is the permeability of free space with value
`\mu_o = 4\pi * 10^(-7) N/A^2`

=>
`\epsilon_a = 4\pi * 10^(-7) * 81800 * 1.28 * 212 * 8.8*10^(-6)`

`\epsilon_a = 2.45*10^(-4)\ V`