Question

A long solenoid has 20 turns cm\(^{-1}\). The current necessary to produce a magnetic field of 20 mT inside the solenoid is approximately

• A. 1 A
• B. 2 A
• C. 4 A
• D. 8 A

Hint:

Use \( B = \mu_0 n I \) for field inside a solenoid. Convert units correctly: turns/cm → turns/m.

Answer 1

The Correct Option is D

Magnetic field inside a long solenoid is given by: \[ B = \mu_0 n I \] Where: - \( B = 20 \, \text{mT} = 20 \times 10^{-3} \, \text{T} \) - \( \mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \) - \( n = 20 \, \text{turns/cm} = 2000 \, \text{turns/m} \) Substituting: \[ 20 \times 10^{-3} = 4\pi \times 10^{-7} \times 2000 \times I \] \[ I = \frac{20 \times 10^{-3}}{4\pi \times 10^{-7} \times 2000} = \frac{20 \times 10^{-3}}{8\pi \times 10^{-4}} \approx \frac{20}{8\pi} \times 10 \approx \frac{200}{8\pi} \approx \frac{200}{25.12} \approx 8 \, \text{A} \]