JEE Main 2023 · 25 January · morning · Single correct · +4 / −1
A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long and 0.2 m in diameter. The magnetic intensity at the center of the solenoid when a current of 2 A flows through it is :
- (a) 1 A m⁻¹
- (b) 2.4×10⁻³ A m⁻¹
- (c) 1.2×10³ A m⁻¹
- (d) 2.4×10³ A m⁻¹
Answer and solution
Answer (c) 1.2×10³ A m⁻¹
Solution
Physics sir · 4 steps
Magnetic intensity H inside a long solenoid is just turns per metre times current, with no μ₀ in it.
- Long solenoid. The tube is 2 m long but only 0.2 m across, so it behaves like a long solenoid. The field inside is uniform and the diameter does not enter the formula.
H = B/μ₀ = nI, n = N/L
- Turns per metre. n = 1200/(2 m) = 600 m⁻¹.
- Put in numbers. H = 600 × 2 = 1200 A m⁻¹.
- So. The magnetic intensity at the centre is 1.2 × 10³ A m⁻¹, which is option (c).
The idea to keep. For a long solenoid, B = μ₀ nI but H = nI. Always divide the total turns by the length first to get n. The diameter only tells you the solenoid is long.
Answer from the NTA final answer key. Solution by PrepWiser.