A thin disk of radius R = 62.5 mm has uniform surface charge density 8.5 nC/m2.

Question

A thin disk of radius R = 62.5 mm has uniform surface charge density 8.5 nC/m2.
Calculate the potential on the axis that runs through the disk center and is perpendicular to the disk face at a distance of 5.0 mm from the disk.

Calculate the potential on the axis that runs through the disk center and is perpendicular to the disk face at a distance of 30.0 mm from the disk.

Calculate the potential on the axis that runs through the disk center and is perpendicular to the disk face at a distance of 62.5 mm from the disk.

Explanation / Answer

given

sigma = 8.5 nC/m^2 = 8.5*10^-9 C/m^2

R = 62.5 mm = 0.0625 m

potentail on the axis of the disk at a distance x,

V = 2*pi*sigma*k*(sqrt(x^2 + R^2) - x)

a) at x = 5 mm = 0.005 m

V = 2*pi*8.5*10^-9*9*10^9*(sqrt(0.005^2 + 0.0625^2) - 0.005)

= 27.7 volts

b) at x = 30 mm = 0.03 m

V = 2*pi*8.5*10^-9*9*10^9*(sqrt(0.03^2 + 0.0625^2) - 0.03)

= 18.9 volts

c) at x = 62.5 mm = 0.0625 m

V = 2*pi*8.5*10^-9*9*10^9*(sqrt(0.0625^2 + 0.0625^2) - 0.0625)

= 12.4 volts

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