How do stationary charged particles interact at a distance with their surroundings?

by emitting protons into the surroundings

by creating magnetic force fields

by breaking up into smaller charges

by way of their electric fields

The answer is: by way of their electric fields.

Explanation:

When it comes to Physics, a "stationary charge" is a particle that is moving. It is not acted upon by a magnetic force because it does not interact with "static magnetic fields."

Although it cannot create magnetic force fields, it can interact at a distance with their surroundings by way of their electric fields. This electric field is a result of imbalance in the electric charges and it doesn't affect magnets. However, this can, somehow, be extended and felt in their environment.

Thus, this explains the answer.