Three wires lie in a plane, placed parallel to one another and equally spaced by 0.20 m. If the wires are oriented up and down on

the page, the right-hand wire carries 100 A to the top, the middle wire 300 A to the bottom, and the left-hand wire carries 200 A to the top. What are the forces per unit length on each of the wires?

Ugh. Such tedium...

First find the magnetic field exerted by the other two wires:
B = (mu)i/2pi r
for example for the 2nd on the left wire-
B = pi4e-7(300)/2pi(.2)
(you can cancel the pi's)
Sum the two B fields (they're opposite direction so careful)
Next find the force/length
F/L = IB
Lather rinse repeat

To determine the forces per unit length on each of the wires, we can use the right-hand rule for determining the direction of the magnetic field around a current-carrying wire.

1. Calculate the magnetic field produced by each wire:
- The right-hand wire carries 100 A to the top, so the magnetic field around it can be calculated using the formula: B = (μ₀ * I) / (2π * r), where B is the magnetic field, μ₀ is the permeability of free space (4π × 10⁻⁷ T⋅m/A), I is the current, and r is the distance from the wire. In this case, r = 0.10 m (half the spacing between the wires).
- Repeat the same calculation for the middle and left-hand wires, using their respective currents and the same distance.
- Note that the direction of the magnetic field will depend on the direction of the current.

2. Determine the direction of the net magnetic field at the location of each wire:
- Since the wires are all parallel and equally spaced, the magnetic fields produced by the wires will be additive or subtractive depending on their directions.
- Consider the direction of each wire's magnetic field and determine the net magnetic field direction for each wire.

3. Calculate the force per unit length on each wire:
- The force per unit length (also known as the magnetic force per unit length or magnetic force density) is given by the formula: F = B * I * d, where F is the force per unit length, B is the magnetic field, I is the current, and d is the length of the wire.
- Use the calculated net magnetic fields and the respective currents to calculate the force per unit length for each wire.

By following these steps, you can calculate the forces per unit length on each of the wires in the given scenario.