Question

Two coils of self-inductance $2mH$and $8mH$are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coil is:

$\begin{align}
  & \text{A}\text{. 10mH} \\
 & \text{B}\text{. 6mH} \\
 & \text{C}\text{. 4mH} \\
 & \text{D}\text{. 16mH } \\
\end{align}$

Answer 1

Hint: We need to know the relationship between the mutual inductance and the self inductance of two coils, now put the values of the self inductance given in the question into that relationship and find the mutual inductance of the coil.

Formula used:
\[M=\sqrt{{{L}_{1}}{{L}_{2}}}\].

Complete step by step answer:
In simple words, the question the two coils are so close to each other that the effective flux of one coil is completely linked with the other coil then what will be the mutual inductance of these coils.
We know the relationship between mutual inductance and self inductance of two coils,
That is,
\[M=\sqrt{{{L}_{1}}{{L}_{2}}}\] , where M is the mutual inductance, and ${{L}_{1}}$is the self inductance of the first coil and ${{L}_{2}}$is the self inductance of the second coil.
Now,
\[M=\sqrt{\left( 2\times {{10}^{-3}} \right)\left( 8\times {{10}^{-3}} \right)}\], here ${{10}^{-3}}$ , is getting multiplied as the unit is in milli henry so we are converting it to henry.
\[M=\sqrt{\left( 16\times {{10}^{-6}} \right)}\],
\[M=\left( 4\times {{10}^{-3}} \right)H\]
Or,
M = 4 mH.

Hence, the correct answer is option C.

Additional Information
Inductance in an electrical circuit is the tendency of an electrical conductor due to which it opposes the change in the electric current flowing through it.
The main operating principle of generators, motors, and transformers are known as mutual inductance.
An electromagnetic coil is an electrical conductor such as wires, which is generally wrapped around a core.

Note:
Inductance in an electrical circuit is the tendency of an electrical conductor due to which it opposes the change in the electric current flowing through it.
The main operating principle of generators, motors, and transformers are known as mutual inductance.
An electromagnetic coil is an electrical conductor such as wires, which is generally wrapped around a core.