Name: Self Induction
Uploaded: 2019-07-19
Duration: 5 min 48 s
Description: This video describes the principle of self induction. It defines self-inductance and gives the formula for the same and derives its SI unit as well.

Question

State Faraday&rsquo;s law of electromagnetic induction. Find the mutual inductance between two long co-axial solenoids.

Accepted Answer

Faraday's Law of electromagnetic Induction:

Whenever magnetic flux linked with circuit changes emf is induced in it.

The induced emf last as long as the change in the magnetic flux continue.

The magnitude of induced emf is directly proportional to the rate of change of magnetic flux linked with the circuit.

Mutual Inductance of two long co-axial solenoids:

Consider two solenoids $S_{1}$ and $S_{2}$ such that the solenoid $S_{2}$ completely surround the solenoid $S_{1}$ . Let length of each solenoid be $l$ and area of cross-section of each solenoid is $A$ . $N_{1}$ and $N_{2}$ are the total number of turns of solenoid $S_{1}$ and $S_{2}$ respectively.

Let current $I_{1}$ be flowing through solenoid $S_{1}$ . Then magnetic field inside the solenoid $S_{1}$ is given by: $B_{1} = \frac{μ_{\circ} N_{1} I_{1}}{l}$ ................. $(1)$

Magnetic flux linked with each tum of solenoid $S_{2}$ is given by: $B_{1} A = \frac{μ_{\circ} N_{1} I_{1}}{l} A$ ............................ $(2)$

Then, total flux linked with $N_{2}$ turns of solenoid $S_{2}$ is given by: $ϕ_{2} = N_{2} B_{1} A = \frac{μ_{\circ} N_{1} N_{2} I_{1} A}{l}$ ............................ $(3)$

So, $ϕ_{2} = M_{12} I_{1}$ ............................ $(4)$

Here, $M_{12} = \frac{μ_{\circ} N_{1} N_{2} A}{l}$ i.e. Coefficient of mutual inductance of solenoid $S_{1}$ with respect to solenoid $S_{2}$ .

Similarly, $ϕ_{1} = M_{21} I_{2}$ , here $M_{21} = \frac{μ_{\circ} N_{1} N_{2} A}{l}$ i.e. Coefficient of mutual inductance of solenoid $S_{2}$ with respect to solenoid $S_{2}$ .

So, the mutual inductance will be $M = \frac{μ_{\circ} N_{1} N_{2} A}{l}$ .

Hence, the mutual inductance between two long co-axial solenoids is $M = \frac{μ_{\circ} N_{1} N_{2} A}{l}$ .

State Faraday’s law of electromagnetic induction. Find the mutual inductance between two long co-axial solenoids.

Important Questions on Electromagnetic Induction

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