Question

The self inductance of a coil having 500 turns is 50mH. The magnetic flux through the cross-sectional area of the coil while the current through it is 8mA is found to be
$\begin{aligned} & a)4\times {{10}^{-4}}Wb \\\ & b)0.04Wb \\\ & c)4\mu Wb \\\ & d)4mWb \\\ \end{aligned}$

Answer 1

In the above question the self inductance of the coil as well how turns does the coil have is given to us. The current in the coil is also given to us. Therefore we will use the equation of flux through the coil when current is passed through the coil in order to determine the magnetic flux across the cross-sectional area of the coil.

Formula used:
$n\varphi =Li$

Complete step by step answer:
Let us say we have a loop having some cross sectional area. If the self inductance of the loop is ‘L’ and the current through it is ‘i’ then we can say that the flux ($\varphi$ )through the coil when the such the current in the coil is constant is given by,
$\varphi =Li$
Now let us say we bend the same coil such that it has ‘n’ number of turns. Therefore the magnetic flux through the entire coil can be considered as flux through the single loop of the coil. Mathematically we can write this also as,
$\varphi =Li$
In the above question it is given to us that the self inductance of the coil is 50mH with 500 turns and the current flowing through it is 8mA. Therefore the flux through the entire coil if equal to,
$\begin{aligned} & \varphi =Li \\\ & \varphi =50\times {{10}^{-3}}H8\times {{10}^{-3}}A \\\ & \Rightarrow \varphi =400\times {{10}^{-6}}Wb \\\ & \therefore \varphi =4\times {{10}^{-4}}Wb \\\ \end{aligned}$

So, the correct answer is “Option A”.

Note:
It is to be noted that when we bend the coil, it's area will decrease. But at the same time its number of turns also increases. Whether the total number of turns increase or decrease is independent provided the coil is the same. Hence In the above solution we have considered the flux to remain the same.