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Electromagnetic Induction — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsElectromagnetic Induction3 Marks
Question
Define the term ‘mutual inductance’ between the two coils.
Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii r1 and r2 (r2 >> r1). Total number of turns in the two solenoids are N1 and N2 respectively.
✓

Answer

Mutual inductance, between a pair of coils, equals the magnetic flux, linked with one of them, due to a unit current flowing in the other.

Alternate Answer

The mutual inductance, for a pair of coils, equals the emf induced, in one of them, when the current in the other coil is changing at a unit rate.

Let a current I2 flow through the outer coil. The magnetic field due to this current

$ = \mu_{o}\frac{\text{N}_{2}}{l}\times\text{I}_{2}$

The resulting magnetic flux linked with the inner coil

$ = \phi_{12} = \text{N}_{1}.\big(\mu_{o}\frac{\text{N}_{2}}{l}\times\text{I}_{2}\big)\times\pi\text{r}_{1}^{2}$

$ = \bigg(\mu_{o}\frac{\text{N}_{1}\text{N}_{2}}{l}.\pi\text{r}^{2}_{1}\bigg)\text{I}_{2}$

= M12 I2

$\therefore\text{M}_{12} = \mu_{o}\frac{\text{N}_{1}\text{N}_{2}}{l}.\pi\text{r}^{2}_{1}.$

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