Case: Read the passage and answer the question.
The number of magnetic field lines crossing a surface is called the magnetic flux. An electric current can be induced in a coil by a flux change produced by another coil in its vicinity or by a flux change produced by the same coil. The former is called mutual induction and the latter is called self-induction.
Consider the following statements:
(A) Magnetic flux is a scalar quantity.
(B) For two long co-axial solenoids, the flux linked with S1 per ampere of current in S2 is equal to the flux linked with S2 per ampere of current in S1.
(C) For two nearby coils, the flux linked with one coil per ampere of current in the other depends on the size of that current.
(D) Placing a soft-iron core inside a coil decreases the flux linked with the coil for the same current.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) and (B) only
Inductance is the flux linkage of a coil per ampere of current. The current may flow in the same coil or in a nearby coil. Inductance depends only on the shape and size of the coils and on the material inside them.
(A) Magnetic flux is a scalar quantity. — True. Flux \( \Phi_B=BA\cos\theta \) is the dot product of two vectors. So it has a magnitude but no direction.
(B) For two long co-axial solenoids, the flux linked with S1 per ampere of current in S2 is equal to the flux linked with S2 per ampere of current in S1. — True. These two ratios are \( M_{12}=N_1\Phi_1/I_2 \) and \( M_{21}=N_2\Phi_2/I_1 \). For long co-axial solenoids both are equal to \( \mu_0n_1n_2\pi r_1^{2}l \).
(C) For two nearby coils, the flux linked with one coil per ampere of current in the other depends on the size of that current. — False. This ratio is the mutual inductance. It depends only on the geometry of the coils and the material in them. It does not depend on the current.
(D) Placing a soft-iron core inside a coil decreases the flux linked with the coil for the same current. — False. Soft iron has a high relative permeability \( \mu_r \). For the same current it makes the field, and so the flux, \( \mu_r \) times larger.
NCERT (2026-27):
Magnetic Flux – “… Magnetic flux is a scalar quantity.”
Mutual inductance – “… we get”
\( M_{12}=M_{21}=M\ \text{(say)} \)\( \qquad (6.12) \)
Inductance – “… We shall see that inductance depends only on the geometry of the coil and intrinsic material properties.”
Self-inductance – “If we fill the inside of the solenoid with a material of relative permeability μr (for example soft iron, which has a high value of relative permeability), then,”
\( L=\mu_r\mu_0n^{2}Al \)\( \qquad (6.16) \)