Question

Two small positively charged spheres have a combined charge of 5.0 * 10^-5 c. if each sphere is repelled from the other by an electrostatic force of 1.0 N when the spheres are 2.0 m apart, what is the charge on each sphere?

Answer 1

Given, `q+q'=5*10^-5C...............1`

And, using `F=(kqq')/r^2` we get,

`qq'=(Fr^2)/k=1*2^2/(9*10^9)=(4/9)*10^-9`

So, `(q-q')^2 =(q+q')^2 -4qq'`

`=25*10^(-10) -(16/9)*10^-9`

`=2.5*10^-9 - 1.78*10^-9`

`=(2.5-1.78)*10^-9`

`=0.72*10^-9=7.2*10^-10`

So, `(q-q')=_-^+2.67*10^-5............................2`

Solving `1` and `2` we get,

`q=3.835*10^-5C` and `q'=1.165*10^-5C` and vice versa, i,e the two charges are of the above mentioned magnitude.