Name: Electric Field: Time Varying Magnetic Field
Uploaded: 2019-07-19
Duration: 8 min 32 s
Description: Did you know that the cause of the movement of charges in a stationary circular conducting coil placed in a time-varying magnetic field is due to an induced...

Question

Explain the phenomenon of mutual induction. Define coefficient of mutual induction. What are its units? Calculate coefficient of mutual inductance between two long solenoids?

Accepted Answer

According to the question,

The phenomenon of mutual induction:- The phenomenon of production of induced $e m f$ In one coil due to change of current in the neighboring coil is called mutual induction.

Definitions of coefficient of mutual induction:- A measure of the induction between two circuits; the ratio of the electromotive force in a circuit to the corresponding change of current in a neighboring circuit.

Unit of mutual induction = Henries.

Coefficient of mutual inductance between two long solenoids:-

Let $S_{1}$ and $S_{2}$ Be two long solenoids of length $l .$ The solenoid $S_{2}$ Is wound closely over the solenoid $S_{1}$ As shown in the given figure,

We know that magnetic field of solenoid $S_{1}$ is given by,

$B_{1} = μ \frac{N_{1}}{l} I_{1} \dots \dots (1)$

Where $N =$ Number of terms,

$B =$ Magnetic field,

$I =$ Current of solenoids

Now the flux linked with solenoid $S_{2}$ Is given by,

$ϕ_{2} = B_{1} A N_{2}$

From $(1)$ We get,

$ϕ_{2} = (μ_{0} \frac{N_{1}}{l} I_{1}) A \times N_{2} \dots \dots (2)$

But we know that,

$ϕ_{2} = M I_{1} \dots \dots (3)$

Where, $M$ Is the coefficient of mutual inductance,

From $(2)$ and $(3)$ We get,

$M I_{1} = \frac{μ_{0} N_{1} N_{2} A I_{1}}{l}$

Therefore,

$M = \frac{μ_{0} N_{1} N_{2} A}{l}$

Therefore, the coefficient of mutual inductance between two given solenoids is $M = \frac{μ_{0} N_{1} N_{2} A}{l}$ .

Explain the phenomenon of mutual induction. Define coefficient of mutual induction. What are its units? Calculate coefficient of mutual inductance between two long solenoids?

Important Questions on Electromagnetic Induction

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