Determining Current in Magnetic Field. Check My Approach!?

Question

Question: two rigid rods are oriented parallel to each other and to the ground. the rods carry the same current in the same direction. the length of each rod is 0.85 m, and the mass of each is 0.073 kg. one rod is held in place above the ground, while the other floats beneath the distance of 8.2 x 10^-3 m. Determine the current in the rods.

My Approach: Ok, I did not have a specific approach. I am confused about the variables...how would you use them in this equation? Force = ILBsin(theta).

i figured force by multiplying (.073)(9.8 m/s^2) = .72 N...i used that in the equation listed above. however, my question is regarding the B and L values. very confusing!??? all help appreciated

Answer 1

The force between parallel wires carrying current I1 and i2 and a distance d apart is

F=L*µ0*I1*I2/(2*π*d); here, the wire currents are the same, so

F=L*µ0*I^2/(2*π*d); This force must balance out the weight of the rod = m*g,

so m*g = L*µ0*I^2/(2*π*d). Solve for I:

I = √[m*g*2*π*d/(L*µ0)]

The result is 185.825 amp.

Check the reference to see how the force equation is derived; the magnetic field a distance r from one wire with current I1 is B=µ0*I1/2*π*r The force on a parallel wire with current I2 and at r=d is B*L*I2.