How many turns should a 10-cm long solenoid have if it is to generate a 1.5 × 10^-3 T magnetic field on 1.0 A of current? A) 12 B) 15 C) 119 D) 1194 E) 3183

Question

Quizplus · Accepted Answer

The magnetic field generated by a solenoid is given by B = μnI, where μ is the permeability of free space, n is the number of turns per unit length, and I is the current flowing through the solenoid. Rearranging this equation to solve for n, we get:

n = B/(μI)

Substituting the given values, n = (1.5 × 10^-3 T)/(4π × 10^-7 T·m/A) × 1.0 A = 119.4 turns/m. To find the total number of turns for a 10-cm (0.1 m) long solenoid, we multiply by the length:

N = nL = 119.4 turns/m × 0.1 m = 11.94 ≈ 12 turns.

Therefore, the best choice is C, 119 turns.

How Many Turns Should a 10-Cm Long Solenoid Have If