JEE Main 2023 · 24 January · evening · Single correct · +4 / −1
A long solenoid is formed by winding 70 turns cm⁻¹. If 2.0 A current flows, then the magnetic field produced inside the solenoid is ____________ (μ₀=4π×10⁻⁷ TmA⁻¹)
- (a) 88×10⁻⁴ T
- (b) 1232×10⁻⁴ T
- (c) 176×10⁻⁴ T
- (d) 352×10⁻⁴ T
Answer and solution
Answer (c) 176×10⁻⁴ T
Solution
Physics sir · 4 steps
Turn 70 turns per cm into turns per metre, then B = μ₀ n I does the rest.
- Field inside solenoid. Inside a long solenoid the field is uniform and depends only on the turns per unit length n and the current I.
B = μ₀ n I
- Convert n to SI. n = 70 turns cm⁻¹ = 70 × 100 = 7000 turns m⁻¹, because μ₀ is in SI units.
- Put in numbers. B = 4π × 10⁻⁷ × 7000 × 2.0 = 5.6π × 10⁻³ T. With π = 22/7, this gives 17.6 × 10⁻³ T.
- So. B = 176 × 10⁻⁴ T, which is option (c).
The idea to keep. For a solenoid, n is turns per metre, not total turns and not turns per cm. Get n into SI first and B = μ₀ n I becomes one line.
Answer from the NTA final answer key. Solution by PrepWiser.