Question

A coil of area \[100\,c{{m}^{2}}\] has $500$ turns, magnetic field of \[0.1{Wb}/{{{m}^{2}}}\;\] is perpendicular to the coil. The field is reduced to zero in $0.1 s$ the induced emf of the coil is:
A. 1 V
B. 5 V
C. 50 V
D. Zero

Answer 1

Hint: This is a direct question. We will substitute the equation of the flux flowing through the circuit in terms of the area of the coil and the magnetic field. Then, we will use this equation in the expression of the emf induced in the coil to find the value of the induced emf.

Formula used:
\[e=N\dfrac{d\phi }{dt}\]
\[\phi =B.A\]

Complete answer:
From given, we have the data as follows.

The area of the coil is, \[A=100c{{m}^{2}}\]
\[A=100\times {{10}^{-4}}{{m}^{2}}\]

The number of turns in a coil, N = 500

The magnetic field, \[B=0.1{Wb}/{{{m}^{2}}}\;\]

The time taken, \[t=(0.1-0)s\]
t = 0.1 s

The formulae used in the calculation purpose are discussed as follows.

The electric flux through the coil is given by the formula,

\[\phi =B.A\]

Where B is the magnetic field and A is the area of the coil.

This formula can be elaborated as follows.

\[\phi =BA\cos \theta \]

Where \[\theta \]is the angle between the magnetic field and the plane.

The emf induced in the coil is given as follows.

\[e=N\dfrac{d\phi }{dt}\]

Where N is the number of turns in the coil.

Now, we will substitute the expression of the flux induced in the above equation.

\[e=N\dfrac{B.A}{dt}\]

Now, we will substitute the values of the number of turns in the coil, the area of the coil, the time taken and the magnetic field to find the value of the emf induced.

\[e=500\dfrac{0.1\times 100\times {{10}^{-4}}}{0.1}\]

Continue further calculation.

\[e=5\]

\[\therefore \] The induced emf of the coil is $5V$.

As, the emf induced in the coil equals the value of $5V$, thus, the option (B) is correct.

Note:
The units of the parameters should be taken care of, as in this case, we have converted the units of the parameters, such as the unit of the area from cm to the meter. The expression of the flux in terms of the area of the coil and the magnetic field should be known.