What Are the Effects of Electric Fields and Charges on a Hollow Sphere?

[aheizler]

Homework Statement

a) Find the electric field inside a charged thing hollow sphere. The radius is R and the charge on the sphere is Q.

b) If a charge q is moved from the center outward to a distance R/2, how much work is done?

c) If the maximum electric field that can be supported in air is 10^4 volts per centimeter, find the maximum potential to which a conducting sphere of radius R=10 cm can be raised. What is the maximum charge?

Homework Equations

I'm not sure about these, but I think these are relevant equations:
E = q/r^2
E = F/q_o
W = integral of force*distance

The Attempt at a Solution

For part a), I think the electric field is 0.
I don't know how to do parts b) and c).

Thank you for the help.

 

[anathema]

Thank you for your question. I would like to help you with your queries.

a) In order to find the electric field inside a charged thin hollow sphere, we can use the Gauss's law. According to this law, the electric field inside a closed surface is equal to the charge enclosed by the surface divided by the permittivity of free space. In this case, the surface is the inner surface of the hollow sphere and the charge enclosed is the charge on the sphere. Therefore, the electric field inside the charged thin hollow sphere is given by:

E = Q / (4πε0R^2)

b) To find the work done, we can use the equation W = qΔV, where q is the charge and ΔV is the change in potential. In this case, the charge is q and the potential at the center of the sphere is 0. Therefore, the work done is:

W = q * (Vfinal - Vinitial)

Since the potential at a distance R/2 from the center is given by V = Q / (4πε0R), the work done is:

W = q * (Q / (4πε0R/2) - 0) = (qQ) / (8πε0R)

c) To find the maximum potential to which a conducting sphere of radius R=10 cm can be raised, we can use the equation E = V / R, where E is the maximum electric field and V is the maximum potential. Therefore, the maximum potential is given by:

V = E * R = (10^4 V/cm) * (10 cm) = 10^5 V

To find the maximum charge, we can use the equation Q = 4πε0RV. Therefore, the maximum charge is given by:

Q = (4πε0R) * (10^5 V) = (8.85 * 10^-12 C^2/Nm^2) * (10^5 V) = 8.85 * 10^-7 C

I hope this helps. Let me know if you have any further questions.