Question

A solenoid with N=500 turns of wire is 5.0 m long and has a radius of 0.2 cm. What current is needed to create magnetic field 3.2 mt at the center of the solenoid?

a. 25 A
b.64 A
c.0.13 A
d. 20 A
e. 0.5 A

Answer 1

The current needed to create a magnetic field of 3.2 mT at the center of a solenoid with 500 turns and 5.0 m in length is approximately 25 A. This is found using the formula B = μ0nI and solving for I. Option a is the correct answer.

Step-by-step explanation:

To determine the current needed to create a magnetic field of 3.2 mT (or 0.0032 T) at the center of a solenoid, we use the formula for the magnetic field inside a solenoid: B = μ0nI, where μ0 is the permeability of free space (μ0 = 4π x 10-7 T·m/A), n is the number of turns per unit length, and I is the current through the solenoid. Given that the solenoid has N = 500 turns and is 5.0 m long, the number of turns per meter is n = N / length = 500 / 5.0 = 100 turns/meter.

Plugging these values into the formula, we get:

0.0032 T = (4π x 10-7 T·m/A) × 100 turns/m × I

Solving for I, we find that:

I = 0.0032 T / ((4π x 10-7 T·m/A) × 100 turns/m)

I = 0.0032 T / (4π x 10-5 T/A)

I ≈ 25 A

Therefore, the correct option for the current needed to create a magnetic field of 3.2 mT at the center of the solenoid is (a) 25 A.