In the figure below, a small, nonconducting ball of mass m = 0.90 mg and charge

Question

In the figure below, a small, nonconducting ball of mass m = 0.90 mg and charge q = 2.50 times 10 -8C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle ? = 10 degree with a vertical, uniformly charged nonconducting sheet (shown in cross section). Considering the gravitational force of the ball and assuming that the sheet extends far vertically and into and out of the page, calculate the surface charge density ? of the sheet. How is the electric field outside an infinite charged nonconductor related to the surface charge density? Did you draw the electrostatic force, the gravitational force, and the force from the string as vectors, with their tails on the ball? Do you see that the net force is zero? Can you relate the forces to the angle ? of the string? T= mg/cos(theta)=(.9e-6 x 9.8)/cos10 = -1.05116187e-5 E = (Tsin(theta)) / q = ((-1.05116187e-5) x sin10)/ 2.5 e-8= 228.7416999 Then I do 1/2pikE = (1 / 2pi 9e9) x 228.7416999 = 4.045041359e-9

Explanation / Answer

ok

as U calculated   E = 228.7416999 N/C

then for surface charge density :::   E = (surface charge density) /(2*epsilon )

                                                (surface charge density) = E*2*epsilon

                                                                                      =228.7416999*2*8.85*10^-12

                                                                                     = 4.048*10^-9 C/m^2

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