Question

Two long, parallel wires are separated by a distance of 2.60 cm. The force per unit length that each wire exerts on the other is 4.30×10^−5 N/m, and the wires repel each other. The current in one wire is 0.520 A.Required:a. What is the current in the second wire? b. Are the two currents in the same direction or in opposite directions?

Answer 1

Answer:

10.75 A

The current is in opposite direction since it causes a repulsion force between the wires

Explanation:

Force per unit length on the wires = 4.30×10^−5 N/m

distance between wires = 2.6 cm = 0.026 m

current through one wire = 0.52 A

current on the other wire = ?

Recall that the force per unit length of two wires conducting and lying parallel and close to each other is given as

$F/l$ = $\frac{u_{0}I_{1} I_{2} }{2\pi r }$

where $F/l$ is the force per unit length on the wires

$u_{0}$ = permeability of vacuum = 4π × 10^−7 T-m/A

$I_{1}$ = current on the first wire = 0.520 A

$I_{2}$ = current on the other wire = ?

r = the distance between the two wire = 0.026 m

substituting the value into the equation, we have

4.30×10^−5 = $\frac{4\pi *10^{-7}*0.520*I_{2} }{2\pi *0.026}$ =  $\frac{ 2*10^{-7}*0.520*I_{2} }{0.026}$

4.30×10^−5 = 4 x 10^-6 $I_{2}$

$I_{2}$ = (4.30×10^-5)/(4 x 10^-6) = 10.75 A

The current is in opposite direction since it causes a repulsion force between the wires.