Magnetism: Forces between two parallel wires

[mikil100]

Homework Statement

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

Homework Equations

[/B]

F=qvBsin(theta)

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.

 

[haruspex]

where I1 is the 8.8 current

You mean 8.2, right?

The denominator in the equation for the field from I1 is 0.088-r

You are asked for the distance from the 8.2A. Isn't that your I1?

Now a charge is placed 5.3cm from the 9.3 A current

Hmm... but how far from the other wire? Is it between them, to the right of the 9.3A, or out of the plane of the wires?

 

[mikil100]

You mean 8.2, right?

You are asked for the distance from the 8.2A. Isn't that your I1?

Hmm... but how far from the other wire? Is it between them, to the right of the 9.3A, or out of the plane of the wires?

My apologies, I will edit the OP. I1 is 8.2A, I2 is 9.3 A, and the distance between the two is 0.088m.

The charge is moving right, and its original location is to the right of i2, at a distance of 0.053cm from I2

 

[haruspex]

My apologies, I will edit the OP. I1 is 8.2A, I2 is 9.3 A, and the distance between the two is 0.088m.

I don't see the correction. It still seems to me your r is the distance from I2, not I1. Are you still getting 0.0452m as the answer?

The charge is moving right, and its original location is to the right of i2, at a distance of 0.053cm from I2

Then your method is fine. I'll check the numbers if you post all your working.

 

[HalfLostAndSearching]

I would like to commend you on your efforts in solving this problem and applying the relevant equations. Your approach and calculations seem to be correct and in line with the principles of magnetism. However, I would suggest double-checking your calculations and units to ensure accuracy. Also, it is always helpful to provide a clear explanation of your reasoning and assumptions for each step in your solution. Overall, your understanding of magnetism and its principles seems to be solid, and with further practice and experience, you will become more confident in your calculations. Keep up the good work!