Question

The self-inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as
(A). l and A increases
(B). l decreases and A increases
(C). l increases and A decreases
(D). Both l and A decreases

Answer 1

Hint: In order to answer this question, we should be having an idea about the concept of solenoid. So, by solenoid, we mean a long insulated wire which is coiled into a cylinder. As soon as direct current is flown, a magnetic field is produced inside the coil. This magnetic field that is produced is uniform in strength and in direction as well. This turns the solenoid into a temporary magnet. There are various factors on which the self-inductance of a solenoid depends. The factors are to be mentioned in the answer.

Complete step-by-step answer:
We should know that the self-inductance of a solenoid depends on various factors. The factors can be known from the formula of solenoid. Here it is:
$L=\mu_0 \mu_r n^2 Al$
In the above formula, n denotes the number of turns per unit length. The value of n can also be written as $\dfrac{N}{l}$.
We should know that, the larger will be the cross sectional area of the solenoid, the larger will be the self-inductance. Similarly, the larger will be the number of turns in a solenoid, the larger will be the self-inductance.
We should know that the self-inductance of a solenoid increases $\mu_r$ times if it is wound over an iron core, the relative permeability of the iron core being $\mu_r$. The solenoid having a cross sectional area of A and length l, experiencing A number of turns and having filled with a material of relative permeability, is already shown in the above-mentioned formula.
So the conclusion that we get from the formula is that the self-inductance L of a solenoid increases as the l decreases and A increases because L and A is directly proportional to each other, but inversely proportional to length.
Hence, we can say that the correct answer is Option B.

Note: As we have seen that the solenoid behaves as a magnet only when the direct passes through it. Therefore, it is quite evident that the magnetic field within the solenoid will depend on the current and the density of the turns. The permittivity or permeability of the medium should also be taken into consideration.