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Question : 16
Total: 26
(a) Define mutual inductance between a pair of coils. Derive an expression for the mutual inductance of two long coaxial solenoids of same length wound one over the other.
OR
(b) Define self-inductance of a coil. Obtain the expression for the energy stored in an inductorL
OR
(b) Define self-inductance of a coil. Obtain the expression for the energy stored in an inductor
Solution:
Definition of mutual inductance
Derivation of mutual inductance for two long solenoids
(i) Mutual inductance is numerically equal to the induced emf in the secondary coil when the current in the primary coil changes by unity.
(ii)
Let a current,i 2
∴ B 2 =
∴
= N 1 A 1 B 2 =
= M 12 i 2
M 12 =
= µ 0 n 2 n 1 A 1 l ( n 1 =
; n 2 =
)
OR
Definition of self inductance
Expression for energy stored
(i) Self inductance, of a coil, is numerically equal to the emf induced in that coil when the current in it changes at a unit rate.
(ii) The work done against back/induced emf is stored as magnetic potential energy.
The rate of work done, when a currenti
= | ε | i = ( L
) i
∴ W = ∫ d W =
L i d i
=
L i 2
Derivation of mutual inductance for two long solenoids
(i) Mutual inductance is numerically equal to the induced emf in the secondary coil when the current in the primary coil changes by unity.
(ii)
Let a current,
OR
Definition of self inductance
Expression for energy stored
(i) Self inductance, of a coil, is numerically equal to the emf induced in that coil when the current in it changes at a unit rate.
(ii) The work done against back/induced emf is stored as magnetic potential energy.
The rate of work done, when a current
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