Four point charges, q , are fixed to the four corners of a square that is 10.3 c

Question

Four point charges, q, are fixed to the four corners of a square that is 10.3 cm on a side. An electron is suspended above a point at which its weight is balanced by the electrostatic force due to the four point charges, at a distance of 16 nm above the center of the square. (The square is horizontally flat, and the electron is suspended 16 nm vertically above the center of the square.)

What is the magnitude of each fixed charge in coulombs? ________ C

What is the magnitude of each fixed charge as a multiple of the electron's charge? _________ e

Explanation / Answer

first we find the angle , = 1.27*10^-5 degree

the resultant force F' = 4Fsin

since the horizontal comonents cancel each other, we added vertical components.

here F = kq(e)/r^2

therefore the resultant force F' = 4*kq(e)/r^2*sin

but F = mg

mg =  4*kq(e)/r^2*sin

q = mg*r^2 sin/4*k*(e)

   = 1.9*10^-31*9.8*r^2*2.218*10^-7/(4*9*10^9*1.602*10^-19)

= 37.2*10^-35 C

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