WOW this problem is making me mad. I know force between two wires is mu*I1*I2*L/2pi*d. Ive used this and tried to find the magnitude but it says its wrong. What Am i doing wrong? I made sure to subtract the two forces one going up and one going down.
There are 3 wires all parallel. Each carries 10 A. The top one is to the right. middle is to the left. and bottom is to the right. Find the force magnitude on the top wire. there Lengths are 50cm.and each are separated by 2cm.
nevermind i got it im just stupid with a calculator i guess.
OK. Glad you were able to figure it out. Thanks for letting us know
To find the magnitude of the force between two parallel wires, you are correct in using the formula:
Force = (μ * I1 * I2 * L) / (2 * π * d)
where μ is the permeability of free space (or the magnetic constant), I1 and I2 are the currents flowing through the wires, L is the length of the wires, and d is the distance between them.
In your case, there are three parallel wires. Considering the top wire, we need to find the net force exerted on it by the other two wires. Since the middle wire carries current in the opposite direction, it will exert a force in the opposite direction as well, while the bottom wire, which carries current in the same direction, will exert a force in the same direction.
To calculate the combined force between the top wire and the middle wire, you will subtract the force exerted by the middle wire from the force exerted by the bottom wire.
Let's calculate the magnitude of the force exerted individually by each wire using the formula above:
1. Force exerted by the top wire on the middle wire:
Force = (μ * I1 * I2 * L) / (2 * π * d)
= (4π × 10^-7 Tm/A * 10 A * 10 A * 0.5 m) / (2π * 0.02 m)
= 10^(-6) Tm/A * 5 m / 0.02 m
= 0.25 N
2. Force exerted by the top wire on the bottom wire:
Force = (μ * I1 * I2 * L) / (2 * π * d)
= (4π × 10^-7 Tm/A * 10 A * 10 A * 0.5 m) / (2π * 0.02 m)
= 10^(-6) Tm/A * 5 m / 0.02 m
= 0.25 N
Since the forces exerted by the middle and bottom wires are equal in magnitude but opposite in direction, their net effect cancels out.
Thus, the force magnitude on the top wire should be the sum of the forces exerted by the middle and bottom wires:
Net Force = Force exerted by the top wire on the middle wire - Force exerted by the top wire on the bottom wire
= 0.25 N - 0.25 N
= 0 N
The net force on the top wire is zero, indicating that the forces exerted by the middle and bottom wires cancel each other out. Therefore, there is no net force on the top wire.