Determine the charge density for each of the following cases (assume that all de
ID: 2001759 • Letter: D
Question
Determine the charge density for each of the following cases (assume that all densities are uniform).
(a) a solid cylinder that has a length L, has a radius R, and carries a charge Q throughout its volume
a.) Q /WL b.) Q /R2L c.) QL/R2 d.)Q /4R2
b) a flat plate (very thin) that has a width W, has a length L, and carries a charge Q on its surface area
a.) QW/ L b.)QL /W c.)3Q /4R3 d.)Q /WL (
c) a solid sphere of radius R carrying a charge Q throughout its volume
a.) Q /WL b.) 3Q /4R3 c.) Q /4R2 d.) Q /R2L (
d) a hollow sphere of radius R carrying a charge Q over its surface area
a.) 3Q /4R3 b.)Q /R2W c.)Q /WL d.) Q /4R2
Explanation / Answer
(A)
volume = pi*R^2*L
density = charge / volume = Q/piR^2L
option (b)
(B)
area = Length*width = LW
density = charge/area = Q/WL
option (d)
(C)
volume = (4/3)pi*R^3
Density = charge/ volume = Q/(4/3)*pi*R^3 = 3Q/4piR^3
option ((b)
(D)
surface area = 4piR^2
density = charge/area = Q/(4pi*R^2)
option (d)
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