Question
Consider a long solenoid of length l and radius r. If n is the number of turns per unit length and _0 is the permeability of free space, the inductance of the solenoid is :
NEET
Physics
Electromagnetic Induction
2026
NEET 2026 (Re-NEET)
NEET Physics Question (2026) — Solution
Options
- A. 2 _0 n^2r^2l
- B. _0 n^2r^2l
- C. _0 n^2r^2l
- D. ( _0/2 )n^2r^2l
Answer
B. _0 n^2r^2l
Step-by-step solution
The magnetic field inside a long solenoid is given by B = _0 n I, where n is the number of turns per unit length and I is the current. The magnetic flux through a single turn of the solenoid is = B A = ( _0 n I)( r^2). The total number of turns in the solenoid of length l is N = n l. The total magnetic flux linkage is = N = (n l)( _0 n I r^2) = _0 n^2 r^2 l I. The self-inductance L is defined by the relation = L I. Substituting the value of , we get L = _0 n^2 r^2 l. Answer: _0 n^2r^2l
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