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The number of turns in an air core solenoid of length 25 cm and radius 4 cm is 100. Its self-inductance will be
(A) $5\times {{10}^{-4}}H$
(B) $2.5\times {{10}^{-4}}H$
(C) $5.4\times {{10}^{-3}}H$
(D) $2.5\times {{10}^{-3}}H$

Last updated date: 24th Jun 2024
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Hint:We know that Solenoid is the generic term for a coil of wire used as an electromagnet. It also refers to any device that converts electrical energy to mechanical energy using a solenoid. The device creates a magnetic field from electric current and uses the magnetic field to create linear motion. Solenoids are the most important components used in solenoid valves to control the flow of liquids and gases. Solenoids are electromechanical devices that convert AC or DC electrical energy into linear motion. Based on this concept we have to solve this question.

Complete step-by-step answer:
We know that in electromagnetism and electronics, inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it.
Inductors are used as the energy storage device in many switched-mode power supplies to produce DC current. The inductor supplies energy to the circuit to keep current flowing during the off-switching periods and enables topographies where the output voltage is higher than the input voltage.
$\text{Inductance = }\!\!\mu\!\!\text{ }{{\text{N}}^{\text{2}}}\dfrac{\text{Area}}{\text{Length}}$
$=\mu {{100}^{2}}\dfrac{\pi {{0.4}^{2}}}{0.25}=2.5\times {{10}^{-4}}H$
Self-inductance is the property of a circuit, often a coil, whereby a change in current causes a change in voltage in that circuit due to the magnetic effect caused by the current flow.
Hence the self-inductance will be $2.5\times {{10}^{-4}}H$.

Hence, the correct answer is Option B.

Note: There are several physical factors which affect the inductance of a coil. They include the number of turns in the coil, the diameter of the coil, the coil length, the type of material used in the core, and the number of layers of winding in the coils. As per specification of Inductors, the temperature coefficient of inductors can be determined by measuring DC resistance of inductors.
All other factors being equal, a greater number of turns of wire in the coil results in greater inductance; fewer turns of wire in the coil results in less inductance. The inductance of a circuit depends on the geometry of the current path as well as the magnetic permeability of nearby materials. Winding the wire into a coil increases the number of times the magnetic flux lines link the circuit, increasing the field and thus the inductance.