How many turns should a 10-cm long ideal solenoid have if it is to generate a 1.5-mT magnetic field when 1.0 A of current runs through it? (μ₀ = 4π × 10^-7 T ∙ m/A) A)12 B)15 C)120 D)1200 E)3200

Question

Quizplus · Accepted Answer

The magnetic field generated by an ideal solenoid is given by the equation:

B = μ₀nI

where B is the magnetic field, n is the number of turns per unit length (also known as the "turns density"), I is the current, and μ₀ is the permeability of free space.

Rearranging this equation to solve for n, we get:

n = B/(μ₀I)

Plugging in the given values, we get:

n = (1.5 × 10⁻³ T) / [4π × 10⁻⁷ T∙m/A × 1.0 A]

n = 3.77 × 10³ turns/m

To find the total number of turns, we need to multiply this by the length of the solenoid:

N = nL

N = (3.77 × 10³ turns/m) × 0.1 m

N = 377 turns

Therefore, the best choice is C, 120 turns.

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