Two long and parallel straight wires A and B carrying currents of 8 ⋅ 0 A and 5 ⋅ 0 A in the same direction are separated by a distance of 4 ⋅ 0 cm. Estimate the force on a 10 cm section of wire A.

To find the force on wire A due to the current in wire B, we can use the formula for the magnetic force between two parallel currents. The force per unit length (F/L) between two long parallel wires is given by:

Formula for Magnetic Force

The formula is:

F/L = (μ₀ * I₁ * I₂) / (2 * π * d)

Where:

• F = force between the wires
• L = length of the wire section
• μ₀ = permeability of free space (approximately 4π × 10^-7 T·m/A)
• I₁ = current in wire A (8.0 A)
• I₂ = current in wire B (5.0 A)
• d = distance between the wires (0.04 m)

Calculating the Force

First, we need to calculate the force per unit length:

F/L = (4π × 10^-7 T·m/A * 8.0 A * 5.0 A) / (2 * π * 0.04 m)

Now, simplifying this:

F/L = (4 × 10^-7 * 8 * 5) / (2 * 0.04)

F/L = (1.6 × 10^-6) / 0.08

F/L = 2.0 × 10^-5 N/m

Finding the Total Force

Now, to find the total force on a 10 cm (0.1 m) section of wire A:

F = (F/L) * L

F = (2.0 × 10^-5 N/m) * 0.1 m

F = 2.0 × 10^-6 N

Final Result

The estimated force on a 10 cm section of wire A is 2.0 μN (microNewtons) in the direction that attracts wire A towards wire B.