Answer:
[tex]5.12\cdot 10^{-4} N[/tex]
Explanation:
The force exerted between two current-carrying wires is given by
[tex]F=\frac{\mu_0 I_1 I_2 L}{2 \pi r}[/tex]
where
[tex]\mu_0[/tex]is the vacuum permeability
I1 and I2 are the two currents
L is the length of the segment of wire on which we want to calculate the force
r is the distance between the wires
In this problem we have:
[tex]I_1 = 12 A\\I_2 = 14 A\\r = 42 cm = 0.42 m\\L = 6.4 m[/tex]
Substituting into the formula, we find:
[tex]F=\frac{(4\pi \cdot 10^{-7})(12)(14)(6.4)}{2 \pi (0.42)}=5.12\cdot 10^{-4} N[/tex]
And since the direction of the two currents is opposite, the force between the wires is repulsive.
