How Does Ampere's Circuital Law Apply to Two Parallel Current-Carrying Wires?

[shrabastee]

Homework Statement

In figure. (i1 and i2 are in the same direction. And the formula for field due to straight long wire is to be used.)

Homework Equations

Magnetic Field(B1) at the conductor carrying I2 current=2i1/d

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

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??

 

[Jhero]

Thank you for bringing this problem to our attention. I would like to offer some guidance and suggestions for solving this problem.

First, let's review the relevant equations for calculating magnetic fields due to straight long wires:

1. Magnetic field (B1) at a point P due to a conductor carrying current i1 = 2i1/d (where d is the distance between the conductor and point P)

2. General magnetic field (B2) at a point P due to a straight long current = 2i/r (where i is the current in the conductor and r is the perpendicular distance between the conductor and point P)

Based on these equations, we can see that the magnetic field at point P due to the conductor carrying i2 current will be given by the following equation:

B2 = 2i2/r (since i2 is the current in this conductor and r is the perpendicular distance between the conductor and point P)

To eliminate the i2 from the expression, we can use the fact that both i1 and i2 are in the same direction. This means that their magnetic fields will add together at point P. Therefore, the net magnetic field at point P due to both conductors will be given by:

Bnet = B1 + B2 = 2(i1 + i2)/r

We can now use this expression to calculate the net magnetic field at point P. I hope this helps you get started on solving this problem. Good luck!