Question

The $5 \times {10^{ - 4}}$ magnetic flux lines are passing through a coil of 100 turns. If the emf induced through the coil is 5mV, then time interval will be:
A. 10 s
B. 0.1 s
C. 0.01 s
D. 0.001 s

Answer 1

Hint: The induced emf is equal to the product of the number of turns of coil and magnetic flux lines and the result is divided by the time interval.

Complete step by step answer:
Faraday’s law states that the induced emf in a closed loop equals the negative of the time rate of change of change of magnetic flux through the loop i.e.,$emf = - \left( {\dfrac{{d\phi }}{{dt}}} \right)$ where $\phi $ is magnetic flux and t denotes time.
If a circuit is a coil consisting of N loops i.e., N number of turns and all are of the same area. So, the total induced emf in the coil is given by the equation $emf = - N\left( {\dfrac{{d\phi }}{{dt}}} \right)$. The negative sign in Faraday’s equation of electromagnetic induction describes the direction in which the induced emf drives a current around a circuit.
The number of magnetic lines of induction inside a coil crossing unit area normal to their direction is called magnitude of magnetic induction or magnetic flux density$\left( \phi \right)$ inside the coil.
Now, $emf = N\left( {\dfrac{{d\phi }}{{dt}}} \right)$
$5 \times {10^{ - 3}} = \dfrac{{100 \times 5 \times {{10}^{ - 4}}}}{t}\left[ {1mV = {{10}^{ - 3}}V} \right]$
$\Rightarrow t = \dfrac{{5 \times {{10}^{ - 2}}}}{{5 \times {{10}^{ - 3}}}}$
$\Rightarrow t = \dfrac{1}{{{{10}^{ - 1}}}}$
$\Rightarrow t = 10\sec $
Therefore, option A is correct.

Note:The magnetic field lines passing through the coil per unit area normal to the direction of area induces an emf in the coil and the negative sign in the formula shows the direction of motion of current in the coil.