Question

A Van 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

Answer 1

The radius r of the metal sphere.

Step-by-step explanation:

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

`E=(Q)/(4\pi \epsilon_oR^2)`

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