Consider a hollow cylinder with inner radies (r in ) of 10 cm, outer radius (r o

Question

Consider a hollow cylinder with inner radies (rin) of 10 cm, outer radius (rout) of 20 cm, and length L. The inner part of the cylinder is given a surface charge density of -n = -1/(pi) nC/m^2. The outer part is given a surface charge density of +n = +1/(pi) nC/m^2.

If the cylinder is made of plastic, let r represent the distance from the axis of the cylinder which has no component along the axis of the cylinder. Additionally, consider L --> infinity.

a) If L must be a finite length, describe when L approaches infinity is valid.

b) Determine the electric field when r < rin

c) Determine the electric field when rin < r < rout

d) Determine the electric field when r > rout

Explanation / Answer

a) When L approaches infinity, ELectric field will be radially outwards from the axis of cylinder.

b) for r < rin

Using GUass LAw, E A = Qin / e0

for r < rin , Qin = 0

so E = 0

c) for rin < r < rout

Qin = surface area x density = (2pi rin L ) (-1/pi) = -2 rin L nC

E ( 2 pi r L) = (-2 x 0.10 x L x 10^-9 ) / (8.854 x 10^-12)

E = - 3.60 / r N/C

d)

for r > rout

Qin = surface area x density = (2pi rin L ) (-1 /pi) +   (2pi rout L ) (1 /pi) = 2 (rout - rin) L nC

E ( 2 pi r L) = (2 x 0.10 x L x 10^-9 ) / (8.854 x 10^-12)

E = 3.60 / r N/C

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