Two long, straight, parallel wires carry current in the same direction. If the wires are 24 cm apart and carry currents of 2.0 A and 4.0 A, respectively, find the force per unit length on each wire?
I'm not really sure how to go about this. I must be spacing or something.
To find the force per unit length on each wire, you can use Ampere's Law.
Ampere's Law states that the magnetic field produced by a long, straight wire is directly proportional to the current and inversely proportional to the distance from the wire.
The magnetic field produced by the first wire at a distance d from the wire can be calculated using the equation:
B1 = μ0 * I1 / (2π * d)
where B1 is the magnetic field produced by the first wire, I1 is the current in the first wire, d is the distance from the first wire, and μ0 is the permeability of free space (4π * 10^-7 T·m/A).
Similarly, the magnetic field produced by the second wire at the same distance d can be calculated using the equation:
B2 = μ0 * I2 / (2π * d)
where B2 is the magnetic field produced by the second wire, I2 is the current in the second wire.
Now, the force per unit length on each wire due to the magnetic field of the other wire can be calculated using the equation:
F = B1 * I2 = B2 * I1
Substituting the equations for B1 and B2, we get:
F = (μ0 * I1 * I2) / (2π * d)
Plugging in the given values:
I1 = 2.0 A (current in the first wire)
I2 = 4.0 A (current in the second wire)
d = 24 cm = 0.24 m (distance between the wires)
μ0 = 4π * 10^-7 T·m/A (permeability of free space)
Calculating F:
F = (4π * 10^-7 T·m/A * 2.0 A * 4.0 A) / (2π * 0.24 m)
= (8π * 10^-7 T·m/A^2) / 0.48 m
= 16π * 10^-7 T/m
So, the force per unit length on each wire is 16π * 10^-7 T/m.