Four solid plastic cylinders all have radius 2.41 cm and length 6.12 cm. Find th

Question

Four solid plastic cylinders all have radius 2.41 cm and length 6.12 cm. Find the charge of each cylinder given the following additional information about each one.

Cylinder (a) carries charge with uniform density 15.9 nC/m2 everywhere on its surface.

Cylinder (b) carries charge with uniform density 15.9 nC/m2 on its curved lateral surface only.

Cylinder (c) carries charge with uniform density 475 nC/m3 throughout the plastic.

Cylinder (d) carries charge with uniform linear density 53.8 nC/m along the length of the plastic.

Explanation / Answer

a) total surface area = curved surface + flat circle

= (2pi r L) + (2 pi r^2)

= (2 x pi x 0.0241 x 0.0612) + (2 x pi x 0.0241^2)

= 9.27e-3 + 3.65e-3 = 12.92 e-3 m^2

charge = surafce density x surface area

= (15.9 x 10^-9 ) x (12.92 x 10^-3) = 2.05 x 10^-10 C

b) charge = surafce density x curved surface area

= (15.9 x 10^-9 ) x (9.27 x 10^-3) = 1.47 x 10^-10 C

c) total volume = pi r^2 h

= pi x 0.0241^2 x 0.0612 = 1.12 x 10^-4 m^3

total charge = 475 x 10^-9 x 1.12 x 10^-4 = 5.30 x 10^-11 C

d) total charge = linear density x length

= 53.8 x 10^-9 x 0.0612 = 3.29 x 10^-9 C

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