Two long parallel wires are separated by 2.0 cm.The current in one of the wires is three times the other current.If the magnitude of the force on a 2.0-m length of one of the wires is equal to 60 $\mu$N,what is the greater of the two currents?
A)2.0 A
B)1.0 A
C)3.0 A
D)9.0 A
E)1.5 A

Question

Quizplus · Accepted Answer

The force between two parallel wires can be calculated using the formula:

F = μ₀I₁I₂L / 2πd

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

In this problem, we are given that the two wires are separated by 2.0 cm, and the force on a 2.0-m length of one of the wires is 60 μN. We can rearrange the formula to solve for one of the currents:

I₂ = 2πdF / μ₀I₁L

Plugging in the given values, we get:

I₂ = 2π(0.02 m)(60×10⁻⁶ N) / (4π×10⁻⁷ T·m/A)I₁(2.0 m)

Simplifying, we get:

I₂ = 3I₁

Therefore, the greater of the two currents is 3A, which is choice C.

Two Long Parallel Wires Are Separated by 2 μ\muμ N,what Is the Greater of the Two Currents? A)2

Two Long Parallel Wires Are Separated by 2 $\mu$ N,what Is the Greater of the Two Currents?
A)2