Answer to Question #208414 in Electric Circuits for Kuina

Question

3. A solid conducting sphere of radius 30cm has a charge of 4 uC. If the potential is zero at infinity. Find the value of the potential at the following distances from the center of the sphere:

a) 45 cm

b) 30 cm

c) 15 cm

Answer 1

Explanations & Calculations

• When it is a conducting sphere, all the charges are constrained on the outside surface of the sphere.
• No charges inside thus, zero-field intensity is observed inside of it.
• According to the equation $\small \vec{E} =\frac{\Delta V}{\Delta x}$, as $\small \vec{E} = 0\implies \Delta V=0$.
• This means that the potential difference is zero & the amount of potential it has at the surface is constant throughout the sphere.
• The potential is equal to what is on the surface.
• And, when gets away from the sphere, a behavior according to Coulomb's law is experienced.

• Then,
• a)

$\qquad\qquad \begin{aligned} \small V&=\small \frac{kq}{r}\\ &=\small \frac{8.98\times10^{-11}Nm^2C^{-2}\times4\times10^{-6}C}{0.45\,m}\\ &=\small \bold{7.98\times10^{-16}\,J/C} \end{aligned}$

• b)

$\qquad\qquad \begin{aligned} \small V&=\small \frac{8.98\times10^{-11}\times4\times10^{-6}}{0.30}\\ &=\small \bold{11.97\times10^{-16}}\,J/C \end{aligned}$

• c)
• It is equal to that at the surface. then,

$\qquad\qquad \begin{aligned} \small V&=\small 11.97\times10^{-16}\,J/C\, \,\,or\, \,\, 11.97\times10^{-16}\,V \end{aligned}$