Question

Ria needs to calculate the number of turns that a solenoid should have, in order to induce a voltage of 50 V provided that the magnetic flux in its cavity changes from 70 mWb to 20 mWb per time 0.20 s. What will be her answer?
1. 50
2. 2
3. 20
4. 200

Answer 1

Correct Answer - Option 4 : 200

Concept:

According to Faraday's law of electromagnetic induction, the induced emf is equal to the rate of change of flux multiplied by the number of turns.

\(E = -N\frac{dϕ}{dt}\)

The negative sign is due to Lenz's law.

Calculation:

Given voltage is 50 V, dϕ = 70 - 20 = 50 mWb, dt = 0.2 s

Total number of turns is:

\(N = \frac{|E|}{|d\phi|}|dt|\)

\(N=\frac{50}{50 \times 10^{-3}}0.2\)

N  = 200