Pressure Applied by Sphere Embedded in Elastic Medium

Consider a sphere embedded inside of an infinite elastic and isotropic medium. If a force $F$ is applied to the ball from a distance (e.g. via a magnetic field), then the ball will in turn apply a force to the surrounding medium. This force acts in 1 direction only (let’s say the $z$ direction).

How do I calculate the pressure at the ball medium interface?

I know that the pressure $p=F/A$, but my understanding is that only the component of the force normal to the surface of the sphere (i.e. parallel to the area vector at each point) will contribute to the pressure. I’m thinking that I need to some how integrate the perpendicular component of the force over the surface area of the sphere. (Or maybe just half the surface area, since only one half of the sphere will be "pushing on" the elastic medium. Can someone help me understand how to set up this integral?