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

The magnitude of force per unit length of one wire on the other is
`2.7945* 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* 10^(-5)\ N` and the direction is towards each other.

Step-by-step explanation:

`\mu_0` = Vacuum permeability =
`4\pi* 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)=(\mu_0 i_1i_2)/(2\pi r)\\ =(4\pi* 10^(-7)* 2.9* 5.3)/(2\pi 0.11)\\ =2.7945* 10^(-5)\ N`

The magnitude of force per unit length of one wire on the other is
`2.7945* 10^(-5)\ N` and the direction is away from one another

`F_(12)=F_(21)=(\mu_0 i_1i_2)/(2\pi r)\\ =(4\pi* 10^(-7)* 2.9* 5.3)/(2\pi 0.11)\\ =2.7945* 10^(-5)\ N`

The magnitude of force per unit length of one wire on the other is
`2.7945* 10^(-5)\ N` and the direction is towards each other.