Van De Graaff Question!?

Question

A van de Graaff generator puts negative charge on a metal sphere. Suppose the radius of the sphere is a = 6.6 cm, and the charge on the sphere is Q = -3.0×10-8 C. Determine the electric field strength at a point 1.0 cm from the surface of the sphere (outside the sphere).

The electric field (E) at a point is the force per unit charge (F/q) on a small hypothetical test charge (q) placed at the point.

Answer 1

For Van de Graaff generators, the charge is distributed uniformly, and it acts as if all of the charge is combined together into a point charge located at the center of the sphere. With that being said, the electric field strength at a distance 1.0 cm from the center of the sphere is:

E = kq / r²

= ((9.0 x 10^9 Nm²/C²) x (-3.0 x 10^-8 C)) / (0.066 m + 0.01 m)²

= 4.7 x 10^4 N/C