The magnetic flux (\( \phi \)) through the area of cross-section of a current-carrying coil is proportional to the current (\( i \)), i.e., \( \phi = Li \)
(A) \( L \) is self-inductance of the coil
(B) The self-inductance of the coil does not depend on its geometry
(C) Self-inductance is the electromagnetic analogue of mass in mechanics
(D) The self-inductance of the coil depends on the permeability of the medium inside coil
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (C) and (D) only
For a long solenoid of \( N \) turns, length \( l \) and cross-sectional area \( A \), filled with a medium of relative permeability \( \mu_r \), the self-inductance is
\( \displaystyle L = \frac{\mu_r \mu_0 N^{2} A}{l} \)
(A) \( L \) is self-inductance of the coil — Correct. The constant of proportionality between the coil's own flux linkage and its current is, by definition, its self-inductance.
(B) The self-inductance of the coil does not depend on its geometry — Incorrect. \( L \) depends on the number of turns, the area and the length of the coil, all of which are its geometry.
(C) Self-inductance is the electromagnetic analogue of mass in mechanics — Correct. Just as mass opposes a change in velocity, self-inductance opposes a change in current (the back emf \( L\,di/dt \)); it plays the role of electrical inertia.
(D) The self-inductance of the coil depends on the permeability of the medium inside coil — Correct. \( L \propto \mu_r \); a soft iron core greatly increases the inductance.
NCERT (2026-27):
Self-Inductance – “… In this case, flux linkage through a coil of N turns is proportional to the current through the coil and is expressed as
\( \displaystyle N\Phi_B \propto I \)
\( \displaystyle N\Phi_B = L\,I \qquad (6.13) \)
where constant of proportionality L is called self-inductance of the coil.”
Self-Inductance – “… The self-inductance of the coil depends on its geometry and on the permeability of the medium. The self-induced emf is also called the back emf as it opposes any change in the current in a circuit. Physically, the self-inductance plays the role of inertia. It is the electromagnetic analogue of mass in mechanics.”