Question

a square coil of side 0.18 and 68 turns is positioned with its plane parallel to 43 T magnetic field. the coil is then turned so that the plane is now perpendicular the magnetic field, in a time of 9ms, what is the magnitude of the induced emf in units of V in the coil

Answer 1

A square coil is placed in a magnetic field of strength 43 T. The number of turns in this coil are 68 and the area of the coil is 0.18x0.18 . Hence because of the magnetic field, magnetic field lines pass through it. So our first step towards solving the question is to find out how many field lines pass through the above mentioned coil. Let to be the number of field lines passing through the coil, it is known as flux.

To find this,

where B is the strength of the magnetic field

           A represents the area through which the field lines pass through

          n is number of turns in the coil

           is angle between the Magnetic field and the object which also plays an important part in deciding how many field lines pass through. So when the object's plane is parallel to the magnetic field, all field lines pass through. But as the inclination is introduced and increased, the number of field lines passing through decreases until it is zero when the plane of object is perpendicular to the field.

In the question, initially the plane of the object is parallel to the field so and , so now

B=43 T

A=0.0324m

n=68

Wb

Now the coil is turned such that it's plane is perpendicular to the magnetic field and now the number of field lines passing through the coil is zero. Hence and . So now.

According to Faraday's Law, if there is any change in the number of magnetic field passing through a coil of wire, this will cause a voltage or emf to be induced in the coil. The value of this emf id represented by E and can be mathematically expressed as

which is the rate of change in magnetic flux with time.

The question says the change in magnetic flux occurred in a time of 9ms. So dt=9ms

Final flux - initial flux

     = -94.7376

Now substituting in,

we get,

Wb= Voltxsecond

This is the magnitude of induced emf in the coil.