Question

Two long, parallel wires are separated by a distance of 3.20 cm. The force per unit length that each wire exerts on the other is 3.30×10−5 N/m, and the wires repel each other. The current in one wire is 0.560 A.
a. What is the current in the second wire?
b. Are the two currents in the same direction or in the opposite direction?

Answer 1

Answer:

(a)The current in the second wire = 9.43 A

(b) The two current are in the opposite direction.

Explanation:

The force per unit length (F/l) on a current carrying conductor = μ₀I₁I₂/2πr

Making I₂ The subject of the equation,

I₂ = [2πr(F/l)]/μ₀I₁.................... Equation 1

Where I₁ = Current in the first wire, I₂ = current in the second wire, μ₀ = permeability of vacuum, r = distance of separation between the two wires.

Given: F/l = 3.30 × 10⁻⁵ N/m, I₁ = 0.56 A, r = 3.20 cm = 0.032 m.

Constant: μ₀= 4π × 10⁻⁷ Am⁻¹.

Substituting these values into equation 1

I₂ = (2π × 0.032 × 3.30 × 10⁻⁵ )/(4π × 10⁻⁷×0.56)

I₂ = (0.032 × 3.3 × 100)/1.12

I₂ = 10.56/1.12

I₂ = 9.43 A

Therefore the current in the second wire = 9.43 A

(b) The two current are in the opposite direction, because the force on each wire repel each other.