Question

A coil of area $100c{m^2}$ has $500$ turns magnetic field of $0.1Wb/{m^2}$ is perpendicular to the coil. The field is reduced to zero in $0.1s$ the induced emf of the coil is
$\left( a \right)\,\,1V$
$\left( b \right)\,\,5V$
$\left( c \right)\,\,50V$
$\left( d \right)\,\,{\text{Zero}}$

Answer 1

Hint: In this question there is only one formula we have to use and that is the relation between the induced emf and the flux. While there are large number of turns than there will be some change in the formula we will use the formula \[\varepsilon = N\dfrac{{\partial {\phi _B}}}{{\partial t}}\] instead of just \[\varepsilon = \dfrac{{\partial {\phi _B}}}{{\partial t}}\] . And, now we just have to put the values in the equation which are given in the equation.

Complete Step by step solution:
Given that there is a coil having an area of $100c{m^2}$ and having $500$ turns magnetic field of $0.1Wb/{m^2}$ is perpendicular to the coil. Then the field is reduced to zero in $0.1s$ then we have to find the induced emf of the coil.
As, we know the relation between the induced emf and flux is given by \[\varepsilon = \dfrac{{\partial {\phi _B}}}{{\partial t}}\] if there are large number of turns then equation changes to \[\varepsilon = N\dfrac{{\partial {\phi _B}}}{{\partial t}}\] , and we will name it equation $1$
And the equation of flux is written as $\phi = BA\cos \theta $
Now by substituting the value of $\phi $ in equation $1$ we will get a new equation
\[ \Rightarrow \varepsilon = N\dfrac{{\partial BA\cos \theta }}{{\partial t}}\] , and we will name it equation $2$
Now substituting the values of \[B\] , \[A\] and \[N\] in equation $2$
We wil get ,
\[ \Rightarrow \varepsilon = \dfrac{{\left( {500\left( {0 - 0.1} \right){{\left( {100 \times {{\left( {10} \right)}^{ - 2}}} \right)}^2}} \right)}}{{0.1}}\]
And on solving the above expression, we get
\[ \Rightarrow \varepsilon = 5 \times {10^4} \times {10^{ - 4}} \times \dfrac{{0.1}}{{0.1}}\]
Further solving more the value will be,
\[ \Rightarrow \varepsilon = 5V\]
So, we will get the value of the induced emf of the coil is \[\varepsilon = 5V\].

Therefore, the option $\left( b \right)$ is correct.

Note: Remember the formula used above like the relation between emf and flux also the change in the formula when there is a large number of turns. Although it is a straightforward question , time may cause some confusion while solving the problem. So, to prevent the confusion be sure what needs to be done to solve the question and always follow step by step procedure.