Question

The north pole of a magnet is brought down along the axis of a horizontal circular coil (figure). As a result, the flux through the coil changes from 0.4 Weber to 0.9 Weber in an interval of half of a second. Find the average emf included during this period. Is the induced current clockwise or anticlockwise as you look into the coil from the side of the magnet?

Answer 1

Hint: To answer this question we should be familiar with that of the equation of emf. Once we write down the equation, we can easily obtain the emf for this question by putting the values that are already mentioned to us. On the basis of the sign of the emf that we will get we can determine the direction of it.

Complete step by step answer:
We know that induced emf is given as:
$\varepsilon = - \dfrac{{d\phi }}{{dt}}$
So now we have to evaluate the formula by putting the values that are mentioned in the question. So here the expression goes:
$
  \varepsilon = - \dfrac{{(0.9 - 0.4)}}{{0.5}} \\
   \Rightarrow \varepsilon = - 1V \\
$
Thus we can say that the EMF that is produced is 1 V and it will oppose the motion of the magnet towards the coil. The direction of the current will be in an anticlockwise direction in this case, in the coil and it will behave as the north pole of the magnet.

Note: For the easy understanding of such questions we should be knowing that if a magnet is moved into a coil of wire, then changing the magnetic field and the magnetic flux through the coil, will generate a voltage in the coil. This is known as the Faraday’s Law.
It is also known that the polarity of the induced emf is such that it will produce a current whose magnetic field will oppose the change that is produced.