Magnetic flux of a loop due to another loop

Question

The scenario is the following, I am given 2 loops with the same radius, r, a distance of d, and same current of I. In the left loop the current goes counter clockwise, in the right loop the current is clockwise. The two loops centers lie on the same axis which are perpendicular to the plane of the loops. I am asked to find the magnetic flux of the left loop due to the current on the right loop.

I know that the magnetic flux of a loop is $\phi=B\pi r^2$, where $B=\dfrac{ \mu_0I}{2R}$ So how exactly do I find the Total magnetic flux on the loop due to the magnetic flux on the other? Am I going to add or subtract? I get confused at this part

Answer 1

If I have understood your question properly, then I think you want to find the magnetic flux through one loop due to the current through the another one. First of all, finding the magnetic field at the center only is not sufficient, and moreover $B=\dfrac{ \mu_0I}{2R}$ is the magnetic field at the center of a loop due to the current through its own. So, you don't need it anyway.

Now, At each point on the circular plane of one loop you need to find the magnetic field due to the current through the another. But this is a tedious job (See here how the magnetic field has been found at the axis only. But for off-axis points the job is tedious). After that you need to integrate the magnetic field over the circular plane.