How to Solve Ampere's Circuital Law Problem with Non-Uniform Magnetic Field?

[shrabastee]

I Posted this earlier, but didn't get a reply =(

1. Homework Statement
Check link. (i1 and i2 are in the same direction. And the formula for field due to straight long wire is to be used.) https://www.physicsforums.com/showthread.php?p=2434701#post2434701


2. Homework Equations

General magnetic field due to a straight long current at point P=μ0i/2πr(r=perpendicular distance between the conductor and the point P)

3. The Attempt at a Solution

I just need some hints to work on. Please help!

EDIT:

These are the steps I came up with:
1)Find B1 due to conductor carrying i1
2)Find B2 due to conductor carrying i2(taking distance as (d-r))
3)Subtract the two to get net field.
4)Integrate.

But how do I eliminate the i2 from the expression??

And B is non-uniform in the problem, so this approach is incorrect anyway=( Please help!

 

[Jhero]

I apologize for the delay in response. I understand that you are looking for some hints to work on the problem mentioned in the link you provided. First, I would suggest checking your approach and equations. The formula you have mentioned is for the general magnetic field due to a straight long current, but in this problem, we are dealing with two currents at different distances from the point P. Therefore, the formula may need to be modified to account for this.

Next, I would suggest drawing a diagram to visualize the problem and see how the two currents are interacting with each other. This can help in understanding the direction and magnitude of the magnetic field at point P.

To eliminate the i2 from the expression, you can use the superposition principle. This principle states that the net magnetic field at a point due to multiple currents is equal to the vector sum of the individual magnetic fields due to each current. Therefore, you can calculate the magnetic field at point P due to each current separately and then add them together to get the net magnetic field.

Lastly, since the magnetic field is non-uniform in this problem, you may need to use an integral to calculate the net magnetic field. I would suggest breaking up the wire into small segments and using the formula for the magnetic field due to a straight long current for each segment, and then integrating over the length of the wire.

I hope these hints will help you in solving the problem. Good luck! And please let us know if you have any further questions.
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