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 $\epsilon = 1.83 *10^{-5} \ V$

Explanation:

From the question we are told that

    The  cross-sectional area is  $A = 2.39 \ cm^2 = \frac{2.39}{10000} = 0.000239 \ m^2$

    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

        $\epsilon = A * \mu_o * n * N \frac{d(I)}{dt}$

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

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

        $\epsilon = 1.83 *10^{-5} \ V$