A large (infinite) rubber sheet which holds a charge per unit area of s = +1µC/m

Question

A large (infinite) rubber sheet which holds a charge per unit area of s = +1µC/m^2 is oriented vertically. A small 30 gram plastic ball is tied to the end of a thread which is attached to the wall. The thread makes a an angle of ? = 30 degrees with respect to the wall.

A) Draw a free body diagram for the ball which shows all forces on it.
B) What is the electric field created by the rubber sheet in terms of s? (Use Gauss' law) C) What is the tension in the thread?
D) What is the charge on the ball?

Explanation / Answer

A) three forces. electric force go outward from the sheet, gravity force and tension of string. B)Gauss's law. s*S/epsilon0=E*2*S so E=s/2epsilon0=56470(V/m) C) tension T we have T*cos30=mg so T=mg/cos30=0.34(N). D) electric force. Fe=T*sin30=0.17(N). F=E*q so q=F/E=3e-6(C)

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