Question

A Van de Graaff generator is a device for generating a large electric potential by building up charge on a hollow metal sphere. A typical classroom-demonstration model has a diameter of 30 cm. a)How much charge is needed on the sphere for its potential to be 500,000V? b) What is the electric field strength just outside the surface of the sphere when it is charged to 500,000V? Please show your work

Answer 1

Answer:

$8.33\times 10^{-6}\ C$

3333333.33 V/m

Explanation:

k = Coulomb constant = $9\times 10^9\ Nm^2/C^2$

d = Diameter = 30 cm

r = Radius = $\frac{d}{2}=\frac{30}{2}=15\ cm$

V = Voltage = 500000 V

Potential in a Van de Graaff generator is given by

$V=\frac{kq}{r}\\\Rightarrow q=\frac{Vr}{k}\\\Rightarrow q=\frac{500000\times 0.15}{9\times 10^9}\\\Rightarrow q=8.33\times 10^{-6}\ C$

Charge needed on the sphere is $8.33\times 10^{-6}\ C$

Electric field is given by

$E=\frac{V}{r}\\\Rightarrow E=\frac{500000}{0.15}\\\Rightarrow E=3333333.33\ V/m$

The electric field strength just outside the surface of the sphere is 3333333.33 V/m