Force between two wires with different currents

Problem

Two parallel wires at $d = 5$ cm carry $I_1 = 8$ A and $I_2 = 12$ A in the same direction. Calculate the force per unit length and state whether the wires attract or repel each other.

Solution

The force per unit length between two parallel current-carrying wires is: $\frac{F}{\ell} = \frac{\mu_0 I_1 I_2}{2\pi d} = \frac{2\cdot10^{-7}\cdot 8\cdot 12}{0{,}05}$ where $\dfrac{\mu_0}{2\pi} = 2\cdot10^{-7}$ was used. $\ev{F/\ell \approx 3{,}8\cdot 10^{-4}\;\text{N/m}}$

Since the currents are in the same direction, the force is ATTRACTIVE: the wires attract each other.

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Topics: Magnetismo Concepts: Forza di Laplace · Campo magnetico