Answer to Question #264716 in Electricity and Magnetism for Faru

Question

1. An infinite non-conducting sheet has a surface charge density 𝜎 = 0.10𝜇𝐶/𝑚2 on one 

side. How far apart are equipotential surfaces whose potentials differ by 50Volts?

2. As a space shuttle moves through the dilute ionized gas of Earth’s ionosphere, the shuttle’s 

potentials is typically changed by -1.0V during one revolution. Assuming the shuttle is a 

sphere of radius 10m, estimate the amount of charge to collects.

3. What are the charge and the charge density on the surface of a conducting sphere of 

radius 0.15m whose potential is 200V with V=0 at infinity?

4. A spherical drop of water carrying a charge of 30pC has a potential of 500V at its surface 

(with V=0 at infinity). (a) What is the radius of the drop? (b) If two such drops of the same 

charge and radius combine to form a single spherical drop. What is the potential at the 

surface of the new drop?

Answer 1

1)

$E=\frac{\sigma}{2\varepsilon_0},$ $\varphi=Ed,\implies$

$d=\frac{2\varphi\epsilon_0}{\sigma}=8.85~mm.$

2)

$q=\frac{\varphi r}k=-1.1\cdot 10^{-9}~C.$

3)

$q=\frac{\varphi r}k=-3.3\cdot 10^{-9}~C,$

$\sigma=\frac q{4\pi r^2}=-11.8\cdot 10^{-9}~\frac C{m^2}.$

4)

a)

$r=\frac{kq}{\varphi}=0.54~mm,$

b)

$\varphi'=\frac{2kq}{\sqrt[3]2 r}=\sqrt[3]4\varphi=794~V.$