Define mutual inductance. Write its SI unit. Derive an expression for…

CBSE Physics class 12 question and answer | (i) Define mutual inductance. Write its SI unit. (ii) Derive an expression for the mutual inductance of a system of two long coaxial solenoids of same length l, having turns N, and N, and of radi r, and re (> r,).

Komal Kohli

March 4, 2024

(i) Define mutual inductance. Write its SI unit.
(ii) Derive an expression for the mutual inductance of a system of two long coaxial solenoids of same length l, having turns N, and N, and of radi r, and re (> r,).

Ans.

(i) Mutual inductance ( $M$ ) is a measure of how much one coil induces an electromotive force (emf) in another coil when the current in the first coil changes. It is measured in henries (H).

(ii) The expression for the mutual inductance ( $M$ ) of a system of two long coaxial solenoids of the same length $l$ , having $N_{1}$ and $N_{2}$ turns, and radii $r_{1}$ and $r_{2}$ ( $r_{2} > r_{1}$ ) is:

$M = l μ ^{0} N ^{1} N ^{2} A ^{2}$

where:

$μ_{0}$ is the permeability of free space,
$N_{1}$ and $N_{2}$ are the number of turns in the solenoids,
$A_{2}$ is the cross-sectional area of solenoid 2,
$l$ is the length of the solenoids.

(i) Define mutual inductance. Write its SI unit. (ii) Derive an expression for the mutual inductance of a system of two long coaxial solenoids of same length l, having turns N, and N, and of radi r, and re (> r,).

Ans.

(i) Mutual inductance (�M) is a measure of how much one coil induces an electromotive force (emf) in another coil when the current in the first coil changes. It is measured in henries (H).

(ii) The expression for the mutual inductance (�M) of a system of two long coaxial solenoids of the same length �l, having �1N1​ and �2N2​ turns, and radii �1r1​ and �2r2​ (�2>�1r2​>r1​) is:

�=�0�1�2�2�M=lμ0​N1​N2​A2​​

where:

�0μ0​ is the permeability of free space,

�1N1​ and �2N2​ are the number of turns in the solenoids,

�2A2​ is the cross-sectional area of solenoid 2,

�l is the length of the solenoids.

This expression represents the mutual inductance between the two solenoids in the given configuration.

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(i) Define mutual inductance. Write its SI unit.
(ii) Derive an expression for the mutual inductance of a system of two long coaxial solenoids of same length l, having turns N, and N, and of radi r, and re (> r,).

(i) Mutual inductance ( $M$ ) is a measure of how much one coil induces an electromotive force (emf) in another coil when the current in the first coil changes. It is measured in henries (H).

(ii) The expression for the mutual inductance ( $M$ ) of a system of two long coaxial solenoids of the same length $l$ , having $N_{1}$ and $N_{2}$ turns, and radii $r_{1}$ and $r_{2}$ ( $r_{2} > r_{1}$ ) is:

$M = l μ ^{0} N ^{1} N ^{2} A ^{2}$

$μ_{0}$ is the permeability of free space,

$N_{1}$ and $N_{2}$ are the number of turns in the solenoids,

$A_{2}$ is the cross-sectional area of solenoid 2,

$l$ is the length of the solenoids.

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