Question

The wire carrying 400 A to the motor of a commuter train feels an attractive force of 4.00×10^(-3) N/m due to a parallel wire carrying 5.00 A to a headlight. How far apart are the wires?

a) 0.02 m
b) 0.04 m
c) 0.06 m
d) 0.08 m

Answer 1

The distance between the wires is 0.02 m, and the currents are in the same direction.

Step-by-step explanation:

To find the distance between the wires, we can use the formula for the magnetic force between two parallel conductors:

F = (μ₀ * I₁ * I₂ * L) / (2πd)

where F is the force, μ₀ is the permeability of free space, I₁ and I₂ are the currents, L is the length, and d is the distance between the wires.

Given that the force is 4.00×10^(-3) N/m, the current in the first wire is 400 A, and the current in the second wire is 5.00 A, we can rearrange the formula to solve for d:

d = (μ₀ * I₁ * I₂ * L) / (2πF)

Substituting the values, we have:

d = (4π * 10^(-7) T·m/A) * (400 A) * (5.00 A) * (1 m) / (2π * 4.00×10^(-3) N/m) = 0.02 m

Therefore, the distance between the wires is 0.02 m. The currents are in the same direction as they are both attractive forces.