Question

A long horizontal wire carries a current of I₁ = 28.0 A. A second wire, made of 0.200 mm diameter copper wire, is 42.0 cm below the first wire and is held in suspension magnetically. What is the magnitude and direction of the current in the bottom wire? Give a + sign if I₂ is parallel to I₁, and a - sign if I₂ is opposite to I₁.
The mass density of Copper is 8.93

Answer 1

area of wire: pi * r^2 = 3.141* 10^-8 m^2

mass of wire per unit length: area * density = 2.805 * 10^-4 g / m

current in the same direction for two parallel wires is attraction, opposite direction is repulsion.

force required per unit length: F' = mass' * acceleration
= (2.805 * 10^-7 kg / cm) * (9.81 m/s^2) = 2.75 * 10^-6 N

F' = mu*I_1*I_2 / (2 * pi * d)

solve for I_2...
I_2 = F' * (2 * pi * d) / (mu * I_1)

= (2.75 * 10^-6)(2)(pi)(42)/(4*pi*10^-7*28)
= 20.625 A