a) radius of the dome r=15 cm
Potential, V=20,000 V
[tex]V=\frac{Q}{4\pi\epsilon_o r}[/tex]
here Q is charge, [tex]\epsilon_o[/tex] is permitivity of vacuum and r is the distance from the charge.
[tex]\Rightarrow Q=V\times4\pi\epsilon_o r[/tex]
[tex]\Rightarrow Q= 20,000\times4\times3.14\times8.85\times10^{-12}\times0.15=3.33\times10^{-7}C[/tex]
b) Electric field (E) strength at the surface of the dome is given by:
[tex]E=\frac{V}{r}\\ \Rightarrow E=\frac{20,000}{0.15}=1.33\times10^{5}V/m[/tex]
c)force on the proton near the surface of the dome:
[tex]F=qE[/tex]
where E is the electric field and q is the charge of proton.
charge of a proton [tex]q=1.6\times10^{-19}C[/tex]
[tex]F=1.6\times10^{-19}\times1.33\times10^{5}=2.218\times10^{-14}N[/tex]
