Two long, straight wires with a current of 8.2A on the left and 9.3A on the right flowing in the same direction. The distance between the wires is 8.8 cm.
a) What is the magnitude of the force per unit length between these two wires both in length and direction
b) How far to the right of the 8.2A wire is the magnetic field due to both currents 0?
c) Now a charge is placed 5.3cm from the 9.3 A current, moving to the right at 76.6 m/s, the charge is 2.9x10^-6C, What is the magnitude of the total magnetic force on this charge
The Attempt at a Solution
For part a I simply used the first formula with using the radius of 0.088m, I is (9.3*8.2), and pretty much just fill in numbers, for an answer I got 1.7x10^-4 N/m, and the wires are attracted. This wasn't difficult.
For part b I used the first formula and set I1=i2, where I1 is the 8.8 current (to the left) and I2 is the 9.3 current, to the right. The denominator in the equation for the field from I1 is 0.088-r, and for the denominator of I2 it was simple r.
Using this method I achieved a distance of r=0.0452m, which seems to make sense to me as it should be somewhere sort of near the middle of the two wires-- using the curly right hand rule I can tell that the field from both of these wires will negate somewhere in the middle of the two wires and since they are close in magnitude it should therefore be in the center. I am just unsure of my method here. I think from a conceptual standpoint I understand what is happening but I am unsure of my math.
For part c I used the principle of super position to add the two magnetic fields together, using the curly right hand rule I assumed the fields would be adding together and not subtracting. This gave me my magentic field for F=qvB.. I als assumed that because the charge is directly right of the 9.3 charge that it is normal to the two wires and therefore receives the full effect of the field. I plugged the values in which resulted in a force of 1.04x10^-8 N
I hope I am on the right track but this is a big question with room for error and I am new to magnetism. Thank you.