The sketch below shows two long conducting wires of mass 05

The sketch below shows two long conducting wires of mass 0.5 kg, suspended on Lm Jong strings. When the wires carry identical currents in the opposite directions, the angle between the strings holding the wires is 10 degrees. What current flows through the wires?

Solution

Here ,

m = 5 Kg

let the current in the wires is I

let the magnetic force on each is F

let the tension in the string is T

T * cos(theta/2) = m * g

T * sin(theta/2) = F

tan(theta/2) = F/(m * g)

F = 4.287 N

F = u0 * I^2/(2 * pi * 2 * 1 * sin(5))

4.287 = 4pi * 10^-7 * I^2/(2 * pi * 2 * sin(5 degree))

solving for I

I = 1933 A

the current in each wire must be 1933 A