Question

Two long, parallel wires are separated by a distance of 2.50 cm . The force per unit length that each wire exerts on the other is 3.90×10−5 N/m , and the wires repel each other. The current in one wire is 0.540 A .A.

(a) What is the current in the second wire?
(b) Are the two currents in the same direction or in opposite directions?

Answer 1

a.9.028A

b. Opposite directions.

Step-by-step explanation:

a. #Assume you have two long, parallel wires separated by a 2.5m distance. Given that
`F/L=3.9* 10^-^5N/m`, the two wires repel each other and the current in one wire is I=0.540A

#Magnitude of the force per unit length of wires is obtained as :

`(F)/(L)=(\mu I\prime I)/(2\pi r)\\\\I \prime =(F/L)(2\pi r/\mu_oI)\\\\=(3.9* 10^-^5N/m)(((2\pi 0.025m))/((4\pi * 10^-^7T.m)(0.54A)))\\\\=9.028A`

Hence the current in the second wire is 9.028A

b.We already know that the two wires parallel and as such attract each other.

-And for two parallel conductors carrying current in opposite directions repel each other.

-Since the two wires repel each other, then the curren in the second wire must flow in the opposite direction of the direction in the first.

# Hence the two wires are in opposite directions.