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

Answer:

a. the current in the other second wire is 820.78 Ampere

b. the two currents are in opposite directions

Explanation:

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

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

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

$I_{2}=\frac{(5.00X10^{-5})(2\pi )(0.023)}{(4\pi X10^{-7})(0.700) }$

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