# A square loop of side 5 centimeters bring moved towards right at a constant speed of 1...

## Question:

A square loop of side 5 cm bring moved towards right at a constant speed of 1 cm/s.The front edge enters the 20 cm wide magnetic field at t=0.

What is the emf induced in the loop at t = 2 s and t = 10 s ?

## Induced EMF

According to Faraday's law, when the magnetic flux through a closed-loop changes, an electromotive force (EMF) is induced in the loop. The EMF will drive a current through the loop. The induced EMF will equal the rate of change of the magnetic flux. The EMF drives the current in such a way that the induced magnetic flux will oppose the applied flux change.

Let us assume the following:

1) The magnetic field is directed into the plane of the paper.

2)The region containing the magnetic field is aligned with its sides parallel to the square.

3) the loop is moving in the plane of the paper.

At {eq}\displaystyle {t=2\ s} {/eq} part of the square loop is inside the magnetic field and part outside. Thus at this instant, the moving loop experiences a flux change. This will induce an emf according to Faraday's law. The emf that is induced between the ends of a conductor of length {eq}\displaystyle {l} {/eq} moving with a speed {eq}\displaystyle {v} {/eq} in a magnetic field of strength {eq}\displaystyle {B} {/eq} when B,l, and v are all mutually perpenicular is given by,

{eq}\displaystyle {V=Blv} {/eq}

Hence,

{eq}\displaystyle { V=B\times 0.05\times 0.01=5B\times 10^{-4}\ V} {/eq}.

At t=10 seconds, the entire loop is inside the magnetic field. The instantaneous flux change it experiences will be zero since it will remain fully immersed in the uniform field for a few more seconds. Hence at {eq}\displaystyle {t=10\ s} {/eq} the induced EMF is zero. 