quantum electrodynamics - Using photons to explain electrostatic force

I am trying to understand the idea of a force carrier with the following example.

Let's say there are two charges $A$ and $B$ that are a fixed distance from each other. What is causing the force on $B$ by $A$?

Classically charge $A$ has an associated electric field which causes a force on $B$. From the standard model, photons are the force carrier for the electromagnetic force. With this view does it mean that $A$ is constantly emitting photons but in a way that the magnetic component cancels out? If that is the case then doesn't that mean that charge $A$ is constantly losing energy?