A thin disc with a circular hole at its center (washer-like) has inner radius R_

Question

A thin disc with a circular hole at its center (washer-like) has inner radius R_1 = 10 cm and outer radius R_2 = 20 cm. The disk has a uniform surface charge density sigma = +2 times 10^-10m. a) Determine the total charge on the disk. b) The disk lies in the xy-plane with its center at the origin. For an arbitrary point on the z-axis, find the magnitude and direction of the electric field due to this ring. c) Find the magnitude and direction of the electric field due to this ring at point (0, 0, 1m).

Explanation / Answer

a] charge q = sigma *area

= 2e-10* pi*(0.20^2-0.10^2)

= 1.885*10^-11

b] electric field E = summation 2 pi k sigma*[1- z/sqrt(z^2+r^2)]

=  2 pi*9e*2e-10*[1- z/sqrt(z^2+0.20^2)] -  2 pi*9e*2e-10*[1- z/sqrt(z^2+0.10^2)]

=  2 pi*9e*2e-10*[z/sqrt(z^2+0.10^2)- z/sqrt(z^2+0.20^2)]

c] E = 2 pi*9e*2e-10*[1/sqrt(1^2+0.10^2)- 1/sqrt(1^2+0.20^2)]

= 4.44*10^-10 N/C

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