A long solenoid (1500 turns/m) carries a current of 20 mA and has an inside diameter of 4.0 cm. A long wire carries a current of 2.0 A along the axis of the solenoid. What is the magnitude of the magnetic field at a point that is inside the solenoid and 1.0 cm from the wire

The magnitude of the magnetic field is 55μT

Explanation:

Given;

number of turns of the solenoid per length, n = N/L = 1500 turns/m

current in the solenoid, I = 20 mA = 20 x 10⁻³ A

diameter of the solenoid, d = 4 cm = 0.04 m

The magnetic field at a point that is inside the solenoid;

B₁ = μ₀nI

Where;

μ₀ is permeability of free space = 4π x 10⁻⁷ m/A

B₁ = 4π x 10⁻⁷ x 1500 x 20 x 10⁻³

B₁ = 3.77 x 10⁻⁵ T

Given;

current in the wire, I = 2 A

distance of magnetic field from the wire, r = 1 cm = 0.01 m

The magnetic field at 1.0 cm from the wire;

The magnitude of the magnetic field;

Therefore, the magnitude of the magnetic field is 55μT