Two small spheres with charges 1.0 C and 2.0 C are situated 10.0 C m apart .Where ( relative to these two)?

Question

should the third sphere of charge 1.0 C be sitiated , so that it experiences no net force?

Answer 1

third charge has to be placed in some point between first two charges.
let's make the arrangement: (x is the distance between 2C and the third charge)
2C -- C -- C
---- x ----
if there is not any net force:
(2C)(C)/x² = (C)(C)/(10-x)²
2(10-x)² = x²
200 - 40x + 2x² = x²
x² - 40x + 200 = 0
a quadratic eq that you can resolve easily

Answer 2

let F13 is the force of the first to the third and F23 is the force of the second to the third
A is where the first is put B : the second and C : the third
according to the porblem we can see that the third must be sittuated so that the three spheres are in one line and according to Newton's law vector F13 = - vector F23 it means that C is within AB because all of them have the positive charge.
F13 = F23 <=> |q1*q3|/(AC)^2 = |q2*q3|/(BC)^2
=> (AC/BC)^2 = q1/q2 = 1/2 =>AC/BC = 1/ 2^(1/2)
=> AC = 10/(1+2^(1/2)) and BC = 10 - AC
now we have the location where the third must be so that it experiences no net force

a^(1/2) means square root of a

Answer 3

i know that it is a little bite late but
all are +ve charges therefore they repair each other , so let there place is like this

(1c) O..............O(2c).............O(1.0c)then
F=k q1 q2/r sq=k 1c*2c/100 =k\50 (force between 1&2c )
k/50=k *1c*2c/r sq =o
when u solve it 10m