An infinitely extensive 4.0 mm thick non-conducting plate is centered on a y-z p
ID: 1278109 • Letter: A
Question
An infinitely extensive 4.0 mm thick non-conducting plate is centered on a y-z plane (the y axis points upward, and the z axis points out of the page). The plate carries a uniformly distributed charge, with a volume charge density of . (a) What is the electric field at ? (Hint: start with the equation for the electric field near an infinite sheet of charge - you are not required to derive it for this problem. Think of the plate as an infinite number of sheets stacked together. Relate the surface charge density of a sheet of charge of thickness dx to the volume charge density. Then integrate to find the net field due to the contributions of all of the sheets.) (b) What is the electric field at ? (c) What would be the answer to part (b) if the plate was made of a conducting material with the same total charge?
Explanation / Answer
(a). Divide the thickness of the plate into stris of width dx
(sigma= ho*dx= 1.5dx)
Electric field due to an infinite sheet = (sigma/2epsilon)
at x = 3mm
Net Electric field = (int_{-2*10^{-3}}^{2*10^{-3}}1.5dx = 1.5(4*10^{-3}) = 6mN/C)
(b). at x = 1mm
Net Electric Field = (int_{-2*10^{-3}}^{1*10^{-3}}1.5dx - int_{1*10^{-3}}^{2*10^{-3}}1.5dx = 1.5(2*10^{-3}) = 3mN/C)
(c). when the plate is made of a conducting material then the answer to part (b) would change because in that case all the charge would reside on the conductor surface and net electric field inside would be equal to zero