A point charge q=−5.0×10−12 C is placed at the center of a spherical conducting shell of inner radius 3.5cm 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?
K: Coloumb's Constant, so
(E*r2)/K = Q
with Q being the derivative of the enclosed q=−5.0×10−12 C
With S = ∫ 4πr2dr
3. The Attempt at a Solution
So if I plug in the values accordingly, I should get:
a) r = 3.5
σ= ((E*r2)/K)/∫ 4πr2dr (integrate from 0 to 3.5)
b) r = 4.5
σ= ((E*r2)/K)/∫ 4πr2dr (integrate from 3.5 to 4.5)
c) Should just be the same as q=−5.0×10−12 C
Before I plug this in to a calculator and get the value, is this correct?
Edit: The integrate sign isn't showing up, so the little circle is actually that.