Question

Calculate the mutual inductance between two coils if a current $10A$ in the primary coil changes the flux by $500\,Wb$ per turn in the secondary coil of $200$ turns. Also determine the induced $e.m.f$ across the ends of the secondary coil in $0.5\,s$ is

Answer 1

Hint: When two coils are brought in proximity with each other the magnetic field in one of the coils tends to link with the other. This further leads to the generation of voltage in the second coil. This property of a coil which affects or changes the current and voltage in a secondary coil is called mutual inductance.
formula used:
$M = \dfrac{Q}{I}$
Where
$M$ is mutual induction
$Q$ is total flux
$I$ is the current
$Q = \phi \times N$
Where
$\phi $ is change in flux
$N$ is number of turns
$e.m.f = M\dfrac{{dI}}{{dt}}$
Where
$e.m.f$ is EMF induced
$\dfrac{{dI}}{{dt}}$is change in current w.r.t time

Complete Step by step answer
$I = 10A$
$t = 0.5$
$\phi = 500\,Wb/turn$
$N = 200$
Total flux $Q = 500 \times 200 = {10^5}\,Wb$
Put value in formula
$M = \dfrac{{{{10}^5}}}{{10}}$
...$M = {10^4}H$
$e.m.f = \dfrac{{{{10}^5} \times 10}}{{0.5}}$
…$e.m.f = 2 \times {10^6}V$

Note : Mutual Inductance is the basic operating principle of the transformer, motors, generators and any other electrical component that interacts with another magnetic field. Then we can define mutual induction as the current flowing in one coil that induces a voltage in an adjacent coil. But mutual inductance can also be a bad thing as “stray” or “leakage” inductance from a coil can interfere with the operation of another adjacent component by means of electromagnetic induction, so some form of electrical screening to a ground potential may be required. The amount of mutual inductance that links one coil to another depends very much on the relative positioning of the two coils. If one coil is positioned next to the other coil so that their physical distance apart is small, then nearly all of the magnetic flux generated by the first coil will interact with the coil turns of the second coil inducing a relatively large emf and therefore producing a large mutual inductance value.