Force per unit length between two wires

Problem

Two parallel straight wires are $10$ cm apart and carry currents $I_1 = I_2 = 5{,}0$ A in the same direction. Calculate the force per unit length between the two wires. What changes if the currents are in opposite directions?

Solution

Each wire is in the field generated by the other; the force per unit length is $\dfrac{F}{L} = \dfrac{\mu_0 I_1 I_2}{2\pi d}$, with $\dfrac{\mu_0}{2\pi} = 2\cdot 10^{-7}$:

$\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d} = \frac{2\cdot10^{-7}\cdot 5{,}0\cdot 5{,}0}{0{,}10}$

$\ev{F/L = 5{,}0\cdot 10^{-5}\;\text{N/m}}$

With currents in the same direction the force is ATTRACTIVE: the two wires attract each other.

If the currents are in opposite directions the magnitude stays the same, but the force becomes REPULSIVE: the wires repel each other.

Links

Topics: Magnetism Concepts: Laplace force · Magnetic field