- #1
doggydan42
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Homework Statement
A point charge ##q = −5.0\times 10^{−12} C## is placed at the center of a spherical conducting shell of inner radius 3.5 cm and outer radius 4.0 cm. The electric field just above the surface of the conductor is directed radially outward and has magnitude 8.0 N/C. (a) What is the charge density on the inner surface of the shell? (b) What is the charge density on the outer surface of the shell? (c) What is the net charge on the conductor?
Homework Equations
$$\vec E = \frac{\sigma}{\epsilon_0}
\\ \sigma = \vec E \epsilon_0 = \frac{q}{4\pi r^2}$$
The Attempt at a Solution
I originally plugged in the charge and the radii into the equation to find the charge density of the inner and outer surfaces. In that case ##r=.035 m## for the inner surface, and ##r=.035+.04 m = .075 m## for the outer surface. This resulted in ##\sigma_{inner}=-3.3\times 10^{-10} \frac{C}{m^2}## and ##\sigma_{outer}=-7.1\times 10^{-11} \frac{C}{m^2}##. When just using the electric field for the outer charge density, The result is ##\sigma_{outer}=-7.1\times 10^{-11} \frac{C}{m^2}##
Since the sphere is a conductor and E is the charge on the surface of a conductor, which is the same when using the radius, would the charge of the inner surface equal 0? Also, would the net charge on the conductor just be ##q=4\pi r_{outer}^2\sigma##?
Thank you in advance.