Question

Two parallel long wires carry the same current and repel each other with a force F per unit length. If both these currents are doubled and the wire separation tripled, the force per unit length becomes:

a.2F/9
b.4F/9
c.2F/3
d.4F/3
e.6F

Answer 1

The force per unit length between two parallel wires can be calculated using a formula. If the currents are doubled and the wire separation is tripled, the new force per unit length becomes 4F/9.

Step-by-step explanation:

The force per unit length between two parallel long wires can be calculated using the formula:

F/1 = (μ₀ * I₁ * I₂ * l) / (2 * π * r)

Where F/1 is the force per unit length, μ₀ is the magnetic constant, I₁ and I₂ are the currents in the wires, l is the length of the wires, and r is the separation between the wires.

In this case, if both the currents are doubled and the wire separation is tripled, the new force per unit length becomes:

F'/(1+2+2) = (μ₀ * 2I₁ * 2I₂ * l) / (2 * π * 3r)

Simplifying the expression, we get:

F'/(5) = (μ₀ * 4I₁ * 4I₂ * l) / (6 * π * r)

Hence, the new force per unit length is 4F / 9.