Name: Faraday’s Law of Induction and Lenz’s Law
Uploaded: 2019-07-19
Duration: 10 min 7 s
Description: Here is an interesting video on electromagnetic induction explaining Faraday's laws of induction and Lenz's law. Get in to it to understand more!

Question

A long solenoid of length

l

, cross- sectional area

A

and having

N_{1}

turns (primary coil) has a small coil of

N_{2}

, turns (secondary coil) wound about its centre. Determine the Mutual inductance (

M

) of the two coils.

Accepted Answer

Both the coils have the same area of cross-section equal to $A$ .

The magnetic flux density at the centre of the long solenoid due to the current $(I)$ flowing through this:

$B = \frac{μ_{\circ} N_{1} I}{l}$

The flux linkage with the smaller coil which is wound at its centre:

$N_{2} φ = B A = \frac{μ_{\circ} N_{1} N_{2} A I}{l}$ .....(i)

Also, as the flux-linkage of the smaller coil is directly proportional to the current flowing through the longer coil hence:

$N_{2} φ = M I$ .....(ii)

where $M$ is mutual inductance which is a constant that depends on the geometrical construction of the coils

On comparing (i) and(ii) we get:

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

Hence, the mutual inductance of the two coils is $\frac{μ_{\circ} N_{1} N_{2} A}{l}$ .

A long solenoid of length $l$ , cross- sectional area $A$ and having $N_{1}$ turns (primary coil) has a small coil of $N_{2}$ , turns (secondary coil) wound about its centre. Determine the Mutual inductance ( $M$ ) of the two coils.

Important Questions on Electromagnetic Induction

Learn and Prepare for any exam you want !

A long solenoid of length l, cross- sectional area A and having N1 turns (primary coil) has a small coil of N2, turns (secondary coil) wound about its centre. Determine the Mutual inductance (M) of the two coils.

Important Questions on Electromagnetic Induction

Learn and Prepare for any exam you want !

A long solenoid of length $l$ , cross- sectional area $A$ and having $N_{1}$ turns (primary coil) has a small coil of $N_{2}$ , turns (secondary coil) wound about its centre. Determine the Mutual inductance ( $M$ ) of the two coils.