Question

A magnetic field of flux density 10T acts normal in a coil of 50 turns having $100c{m^2}$ an area. The e.m.f. induced if the coil is removed from the magnetic field in 0.1 seconds is:
A) 50V
B) 60V
C) 80V
D) 40V

Answer 1

Hint: The full form of EMF is electromotive force. It is defined as the electric potential that is produced by the electrochemical cell. Its unit is volt. Electromotive force is independent of the circuit resistance.

Complete step by step solution:
Given data:
The magnetic flux density, B = 10 T
N = 50 turns
Area, $A = 100c{m^2} = {10^{ - 2}}{m^2}$
Time change,dt = 0.1 sec
e. m. f induced in the coil =?
We know that $\phi = {\rm N}{\rm B}{\rm A}\cos \theta $
$\Rightarrow {\phi _1} = {\rm N}{\rm B}{\rm A}\cos \theta = NBA\cos 0 = NBA$ $\left( {\because \cos 0 = 1} \right)$
Thus substituting the values of N, B, and A we get
$\Rightarrow {\phi _1} = 50 \times 10 \times 1{0^{ - 2}} = 5Wb$
It is given that the coil is removed from the magnetic field. Then B = 0.
Hence ${\phi _2} = 0$
\[\therefore {\phi _2} - {\phi _1} = d\phi \]
\[ \Rightarrow d\phi = \left( {0 - 5} \right) = - 5Wb\]
We also know that e.m.f induces is given by the formula,
$\Rightarrow e.m.f = \dfrac{{d\phi }}{{dt}}$
$ \Rightarrow e.m.f = \dfrac{{ - 5}}{{0.1}} = 50V$
Thus the e.m.f induced in the coil is 50 V.

Hence the correct option is A.

Note: 1. Electromotive force can also be defined as the work done on the unit charge. In general, it remains constant. EMF can be negative.
2. The magnetic field, electric field, and gravitational field are caused by the electromotive force.
3. For the conversion of energy from one form to another form, in general, a battery or a generator will be used. Thus in these, one terminal will act as positively charged while the other terminal will act as negatively charged, and thus the EMF is the work done on the unit electric charge.
4. The field that passes through space thus making the magnetic force to move the electric charge is called the magnetic field. The unit of the magnetic field is Tesla.