Question

What is the magnitude of the emf induced in the secondary winding at the instant that the current in the solenoid is 3.2 A

Answer 1

Complete Question

A very long, straight solenoid with a cross-sectional area of 2.39cm2 is wound with 85.7 turns of wire per centimeter. Starting at t= 0, the current in the solenoid is increasing according to i(t)=( 0.162A/s2) t2. A secondary winding of 5 turns encircles the solenoid at its center, such that the secondary winding has the same cross-sectional area as the solenoid. What is the magnitude of the emf induced in the secondary winding at the instant that the current in the solenoid is 3.2A ?

Answer:

The value is
`\epsilon =  1.83 *10^(-5) \  V`

Step-by-step explanation:

From the question we are told that

The cross-sectional area is
`A = 2.39 \ cm^2 = (2.39)/(10000) = 0.000239 \ m^2`

The number of turns is
`N = 85.7 \ turns/cm = 8570 \ turns / m`

The initial time is t = 0s

The current on the solenoid is
`I(t)   = (0.162 \ A/s^2) t^2`

The number of turns of the secondary winding is
`n =  5 \ turns`

Generally At I = 3.2 A

`3.2 =  (0.162 )t^2`

=>
`t^2  =  19.8`

=>
`t =  4.4 \  s`

Generally induced emf is mathematically represented as

`\epsilon  = A *  \mu_o *  n *  N  (d(I))/(dt)`

`\epsilon  =  0.000239 *  4\pi * 10^(-7) *  8570 * 5 *  (0.162) * 2t`

`\epsilon  =  0.000239 *  4\pi * 10^(-7) *  8570 * 5 *  (0.162) * 2 *  4.4`

`\epsilon =  1.83 *10^(-5) \  V`