Question

Given that q=+12μC, find the distance from q1 where q2 experiences a net electrostatic force of zero. (The charges q1 and q3 are separated by a fixed distance of 42 cm .)

Answer 1

Missing information in the text of the problem: q3=3 q1 = 3q

We can solve the problem by solving a system of two equations. In the first one, we write that the electrostatic force between charge 1 and 2 is equal to the force between charge 2 and 3. In the second equation, we write that the sum of the distances q1-q2 and q2-q3 is equal to 42 cm:

`k_e (q_1 q_2)/(r_(12)^2)=k_e (q_2 q_3)/(r_(23)^2)`

`r_(12)+r_(23)=0.42~m`
From the second equation we write

`r_(12)=0.42-r_(23)`
While we can rewrite the first equation as

`(q)/(r_(12)^2)= (3q)/(r_(23)^2)`
Substituting and solving, we find

`r_(23)=0.99~m` or
`r_(23)=0.27~m`. With the first solution,
`r_(12)` would be negative, which doesn't make sense; therefore we must consider only the second solution, and we have:

`r_(23)=0.27~m`

`r_(12)=0.42-r_(23)=0.15~m`