Question

Two long, straight wires are parallel to each other. The wires carry currents of different magnitudes. If the amount of current flowing in each wire is doubled, the magnitude of the force between the wires will be a) twice the magnitude of the original force. b) four times the magnitude of the original force. c) the same as the magnitude of the original force. d) half of the magnitude of the original force.

Short answer

Answer: The force between the parallel wires becomes four times the magnitude of the original force.

Step-by-step solution

Recall the formula for the magnetic force between two wires

The magnetic force F between two long parallel wires carrying currents I1 and I2 and separated by a distance d is given by the formula: F = (μ₀ * I1 * I2 * L) / (2 * π * d) where μ₀ is the permeability of free space, L is the length of the wires, and π is a constant.

Analyze the situation when the current is doubled in each wire

Let's denote the original currents in the two wires as I1 and I2, and the original force as F₁. If we double the currents in both wires, the new currents will be 2 * I1 and 2 * I2. The new force will be denoted as F₂.

Calculate the new force F₂

Plug the new currents into the force formula: F₂ = (μ₀ * (2 * I1) * (2 * I2) * L) / (2 * π * d) F₂ = 4 * (μ₀ * I1 * I2 * L) / (2 * π * d)

Compare F₂ with the original force F₁

The original force F₁ = (μ₀ * I1 * I2 * L) / (2 * π * d) From step 3, F₂ = 4 * F₁ So, when the currents in both wires are doubled, the force between them becomes four times the original force. Therefore, the correct answer is: b) four times the magnitude of the original force.