Question

Two long, parallel wires are separated by a distance of 2.30 cm . The force per unit length that each wire exerts on the other is 5.00×10−5 N/m , and the wires repel each other. The current in one wire is 0.700 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. the current in the other second wire is 820.78 Ampere

b. the two currents are in opposite directions

Step-by-step explanation:

a. the current in the second wire is given by the expression for the force per unit lenght between two wires

`(F)/(l) = (U_(0)I_(1) I_(2)  )/(2\pi r)`

where
`U_(0) = 4\pi X10^(-7)`

substituting all these values into the expression for the force per unit length and then making
`I_(2)` the subject

Note: convert 2.3 cm to meters = 0.023 meters

`5.00X10^(-5) =(4\pi X10^(-7) )(0.700)I_(2)  / 2\pi (0.023)`

making
`I_(2)` subject

`I_(2)=((5.00X10^(-5))(2\pi )(0.023))/((4\pi X10^(-7))(0.700) )`

simplifying will give

`I_(2) =8.22 A`

b. the force is attractive if the currents are in the same direction and repulsive if the force are in opposite directions