Four solid plastic cylinders all have radius 2.73 cm and length 5.94 cm. Find th

Question

Four solid plastic cylinders all have radius 2.73 cm and length 5.94 cm. Find the charge of each cylinder given the following additional information about each one. Cylinder (a) carries charge with uniform density 15.8 nC/m^2 everywhere on its surface. Cylinder (b) carries charge with uniform density 15.8 nC/m^2 on its curved lateral surface only. Cylinder (c) carries charge with uniform density 535 nC/m^3 throughout the plastic. Cylinder (d) carries charge with uniform linear density 50.6 nC/m along the length of the plastic.

Explanation / Answer

(a) area = 2 * (circle at ends) + lateral curved side = 2 * (pi * 2.73cm ^ 2) + (2 * pi * 2.73cm * 5.94cm)

= 46.80 cm2 + 101.8377 cm2 =148.63 cm2 = 0.014863 m2

hence charge on the cylinder = charge density * area

= 15.8 nC/m2 * 0.014863 m2 =0.2348 nC or 0.2348 x 10-9 C...........Ans.

(b) area = just lateral curved side = rectangle with length equal to the circle perimeter and width equal to

= (2 * pi * 2.73cm) * 5.94cm = 101.83 cm2 =0.010183 m2

hence charge on the cylinder = charge density * area

= 15.8 nC/m2 * 0.010183 m2 =0.1609 nC or 0.1609 x 10-9 C...........Ans.

(c) charge density is given as charge per unit volume. find the total charge by multipling the density by the volume. volume = (area of circle) * height = (pi * 2.73cm ^2) * 5.94cm

= 139.00 cm3 =1.39 x 10-4 m3

hence charge on the cylinder = charge density * volume

= 535 nC/m3 * 1.39 x 10-4 m3 =0.0743 nC or 0.0743 x 10-9 C...........Ans.

(d) Charge on the cylinder = charge density * length

= 50.6 nC/m * 2*5.94 x 10-2 m=6.011 nC or 6.011 x 10-9 C...........Ans.

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