Solenoids: A solenoid with 400 turns has a radius of 0.040 m and is 40 cm long. If this solenoid carries a current of what is the magnitude of the magnetic field near the center of the solenoid? (μ₀ = 4π × 10^-7 T ∙ m/A)

Question

Quizplus · Accepted Answer

The magnetic field near the center of a solenoid is given by the formula:

B = μ0nI

where:
μ0 = 4π × 10-7 T ∙ m/A (permeability of free space)
n = number of turns per unit length
I = current

We first need to calculate n, which is the number of turns per unit length. The given solenoid has 400 turns and is 40 cm long, so the number of turns per unit length is:

n = 400 / 0.40 = 1000 turns/m

Now we can calculate the magnetic field:

B = μ0nI = (4π × 10-7 T ∙ m/A) × (1000 turns/m) × 11 A
B = 15 mT

Therefore, the magnitude of the magnetic field near the center of the solenoid is 15 mT, so the best choice is C.

Solenoids: a Solenoid with 400 Turns Has a Radius of 0.040