Question

Two coils of self-inductance 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:
A. 10 mH
B. 6 mH
C. 4 mH
D. 16 mH

Answer 1

Hint: In this question we have been asked to calculate the mutual inductance between two given coils of 2mH and 8mH. We know that mutual inductance is defined as the property of coil due to which it opposes the change of current in the other coil. We have been given self inductance of two coils. Therefore, we shall use the equation for mutual inductance of two coils.
Formula Used: \[M=\sqrt{{{L}_{1}}{{L}_{2}}}\]
Where,
M is the mutual inductance
\[{{L}_{1}},{{L}_{2}}\] is the self-inductance of two coils.

Complete answer:
Mutual induction is defined as the interaction of the magnetic field of one coil with another coil as it induces a voltage in the other coil. We know that the inductor generates emf in itself when the magnetic field around its turns is changed. Self-inductance is the process of inducing this such emf in the same circuit through which the current is changing.
Now, we know from the equation,
\[M=\sqrt{{{L}_{1}}{{L}_{2}}}\]
We have been given,
\[{{L}_{1}}=2mH\] and \[{{L}_{2}}=8mH\]
Therefore,
\[M=\sqrt{2\times 8}\]
On solving,
\[M=4mH\]

Therefore, the correct answer is option C.

Note:
Positioning the of the two coils is an important factor in determining the amount of mutual inductance. If the distance between two coils is physically small, then magnetic flux generated by the coil will interact with others and give a large value of mutual inductance and vice versa. The equation of magnetic induction between two coils assumes that there is absolutely no flux leakage and that there is complete magnetic coupling. However, in reality there is always some loss in magnetic coupling due to leakage and position.