Physics Q5 – NEET-UG 2026

Consider a long solenoid of length

l

and radius

r

. If

n

is the number of turns per unit length and

μ_{0}

is the permeability of free space, the inductance of the solenoid is :

Clue 1 of 3: Fundamental Concept

The self-inductance of a solenoid depends on its physical dimensions and the permeability of the core material.

🥷

Ninja Strategy•Formula Component Check

Quickly verify if the essential components of the inductance formula, especially the area term $π r^{2}$ , are correctly represented in the options.

🧠 Full Solution Path

Step 1: Recall the Formula for Solenoid Inductance✦ Active

The self-inductance $L$ of a long solenoid is given by the formula:

L = μ_{0} n^{2} A l

Where $μ_{0}$ is the permeability of free space, $n$ is the number of turns per unit length, $A$ is the cross-sectional area, and $l$ is the length of the solenoid.

Step 2: Calculate the Cross-sectional Area○ Expand

Given that the solenoid has a radius $r$ , its cross-sectional area $A$ is that of a circle:

A = π r^{2}

Step 3: Substitute Area into Inductance Formula○ Expand

Substitute the expression for $A$ into the inductance formula from Step 1:

L = μ_{0} n^{2} (π r^{2}) l

L = μ_{0} π n^{2} r^{2} l

This result matches option (1).

💡 Teacher's Secret Hint

Ensure all given parameters are correctly identified and used in the formula.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Physics Question 5 – NEET-UG 2026

Clue 1 of 3: Fundamental Concept

🧠 Full Solution Path