Question

1) (Modified problem 21.58) A large room has a square floor, length 6.00 m to a side. Due to static electricity (and improper construction practices), the surface of the floor carries a small excess positive charge, uniformly distributed over its area. A speck of dust with charge 15.0 uC and mass 5.00 g hovers, suspended over the floor by its electrostatic n from the floor (located close to the floor; not near one of the edges of the room). What is the total charge Q of the floor? (You will need to account for both the weight and electric force on the speck of dust.

Answer 1

Here gravitational force is balanced by electrostatic force as shown in below image.

Electric field due to a square sheet (E) E = sigma/epsilon_0 [sigma is surface charge density] epsilon_0 = 8.85 times 10^-12 m = 5 times 10^-3 kg q = 15 times 10^-6 C mg = qE Therefore 5 times 10^-3 times 9.8 = 15 times 10^-6 times Q/A epsilon_0 [A is area of square] 5 times 10^-3 times 9.8 = 15 times 10^-6 times Q/36 times 8.85 times 10^-12 Q = 1.040 times 10^-6 C Therefore Q = 1.04 mu C