Question

A small, nonconducting ball of mass m=1.0mg and charge q=2.0*10^-8 C (distributed uniformly through it's volume) hangs from an insulated thread that makes an angle theta = 30 degrees with the 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.

Answer 1

Calculate the E field due to the infinite sheet using Gauss' Law. Express it in terms of the charge density, sigma. The horizontal electrical force on the ball equals the horizontal component of the string tension, which is M g tan 30

E q = M g tan 30

sigma*q/(2*epsilono) = M g tan 30

sigma = 2 epsilono * M g tan 30/q

Answer 2

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