Question

Ask Your Teacher Two long, straight wires are parallel and 11 cm apart. One carries a current of 2.9 A, the other a current of 5.3 A. (a) If the two currents flow in opposite directions, what is the magnitude (in N/m) and direction of the force per unit length of one wire on the other? magnitude N/m direction (b) What is the magnitude (in N/m) and direction of the force per unit length if the currents flow in the same direction? magnitude N/m direction

Answer 1

Answer:

The magnitude of force per unit length of one wire on the other is $2.7945\times 10^{-5}\ N$ and the direction is away from one another

The magnitude of force per unit length of one wire on the other is $2.7945\times 10^{-5}\ N$ and the direction is towards each other.

Explanation:

$\mu_0$ = Vacuum permeability = $4\pi\times 10^{-7}\ N/A^2$

$i_1$ = Current in first wire = 2.9 A

$i_2$ = Current in second wire = 5.3 A

r = Gap between the wires = 11 cm

Force per unit length

$F_{12}=F_{21}=\frac{\mu_0 i_1i_2}{2\pi r}\\ =\frac{4\pi\times 10^{-7}\times 2.9\times 5.3}{2\pi 0.11}\\ =2.7945\times 10^{-5}\ N$

The magnitude of force per unit length of one wire on the other is $2.7945\times 10^{-5}\ N$ and the direction is away from one another

$F_{12}=F_{21}=\frac{\mu_0 i_1i_2}{2\pi r}\\ =\frac{4\pi\times 10^{-7}\times 2.9\times 5.3}{2\pi 0.11}\\ =2.7945\times 10^{-5}\ N$

The magnitude of force per unit length of one wire on the other is $2.7945\times 10^{-5}\ N$ and the direction is towards each other.