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What is the surface charge density of the drum?
The electric field just above the surface of the conducting charged drum of a photocopying machines has a magnitude of 2.2 X105 N/C. The drum has a length of 58 cm and a radius of 19 cm.
(a) What is the surface charge density of the drum? (You can ignore any edge effects.)
(b) What is the total charge on the drum?
(c)The manufacturer wishes to produce a desktop version of this copier. This means we must cut the length of the drum down to 29.00 cm and the radius of the drum must be cut to 12.67 cm. What must be the charge on the drum if we wish to keep the electric field at the surface of the drum unchanged?
(a) Gauss' law says integral(E dA) = Q/e0, where e0 is the permittivity of free space. You don't specify the geometry of the field, but if it's radially symmetric then
dQ/dA = e0 E = (9e-12 F/m)(2.2 X105 N/C)
Q = (2.2 X105 N/C)pi(0.19m)^2(0.58m) (9e-12 F/m)
(b) Q (12.67/19)^2 (29/58)
veddy gut, veddy gut indid.
m
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