Magnetic Flux through 1 loop due to current on the other

[lion_]

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 $$B=\dfrac{\mu_0 I}{2R}$$ So how exactly do I find the Total magnetic flux on the loop due to the magnetic flux on the other? Since the current is opposite I will be subtracting the 2 fluxes.

So $$\phi_{self}=\phi_L-\phi_R$$ which is $$ \dfrac{\mu_0I}{2r} \pi d^2 - \dfrac{\mu_0I}{2r}\pi d^2=0$$ I don't think this makes much sense to me...

Homework Equations

The Attempt at a Solution

 

[mfb]

I am asked to find the magnetic flux of the left loop due to the current on the right loop.

I think this is "without the flux from the current in the right loop".

The formula you used is valid inside the considered field-generating loop only, not for other areas.

Do you know how to calculate the magnetic field of a loop for an arbitrary point in space?