Question

The dome of a van de graaff generator has a diameter of 30 cm and is at a potential of +20 000V. Calculate :

a) the charge on the dome
b) the electric field strength at the surface of the dome
c) the force on a proton near the surface of the dome

Answer 1

a) radius of the dome r=15 cm

Potential, V=20,000 V

`V=(Q)/(4\pi\epsilon_o r)`

here Q is charge,
`\epsilon_o` is permitivity of vacuum and r is the distance from the charge.

`\Rightarrow Q=V*4\pi\epsilon_o r`

`\Rightarrow Q= 20,000*4*3.14*8.85*10^(-12)*0.15=3.33*10^(-7)C`

b) Electric field (E) strength at the surface of the dome is given by:

`E=(V)/(r)\\ \Rightarrow E=(20,000)/(0.15)=1.33*10^(5)V/m`

c)force on the proton near the surface of the dome:

`F=qE`

where E is the electric field and q is the charge of proton.

charge of a proton
`q=1.6*10^(-19)C`

`F=1.6*10^(-19)*1.33*10^(5)=2.218*10^(-14)N`