Avan de graaff generator causes a total charge q to build up on a metal sphere of radius r. which variable does not affect the electric field at a distance r from the center of the metal sphere? assume r> r.

the distance r from the center of the metal sphere
the magnitude of the charge q
the radius r of the metal sphere
the sign of the charge q

The radius r of the metal sphere.

Explanation:

From Gauss's law we know that for a spherical charge distribution with charge , the electrical field at distance from the center of the sphere is given by

What is important to notice here is that the radius of the sphere does not matter because any test charge sitting at distance feels the force as if all the charge were sitting at the center of the sphere.

This situation is analogous to the gravitational field. When calculating gravitational force due to a body like the sun or the earth, we take not of only the mass of the sun and the distance from it's center; the sun's radius does not matter because we assume all of its mass to be concentrated at the center.