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Gauss' law

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A small nonconducting ball of mass m=1.0mg and charge q=2x10^-8C(distributed uniformly through its volume) hangs from an insulating thread that makes an angle of 30 degrees with a vertical, uniformly charged nonconducting sheet. Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and out of the page, calculate the surface charge density of the sheet?

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Solution Preview

Lets name the angle of the thread with the vertical: a = pi/6 (30 degrees) and the surface density of electric charge on the sheet be b (measured in C/m^2)

The forces acting on the ball are:
The vertical force of gravitation:
F_g = mg
And the horizontal electric ...