Answer to Question #153976 in Electricity and Magnetism for Viccy

Question

In a 100 turn coil, if the flux through each turn is (t3 - 2t)mWb, the magnitude of the induced emf in the coil at a time of 4 sec is

Answer 1

We can find the induced emf from the Faraday’s law of induction. It states that the emf is given by the rate of change of the magnetic flux:

$$\Epsilon=-N\dfrac{d\Phi_B}{dt},$$

here, $\Epsilon$ is the induced electromotive force, $\Phi_B$ is the magnetic flux through a single turn of coil and $N$ is the number of turns of coil.

Let’s substitute $N$ and $\Phi_B$ into the last formula and find the magnitude of induced electromotive force:

$$\Epsilon=(-100)\cdot\dfrac{d}{dt}(t^3-2t)\ mWb,$$ $$\Epsilon=(-100)\cdot(3t^2-2)\ mWb.$$ $$\Epsilon(t=4\ s)=|(-100)\cdot(3\cdot(4\ s)^2-2)\cdot10^{-3}\ Wb|=4.6\ V.$$

Answer:

$\Epsilon(t=4\ s)=4.6\ V.$