Question

A point charge 25q is 2.0m away from a point charge 9q. Where should a 3rd charge be placed so the net forces on it are zero?

Answer 1

is q supposed to be an arbitrary unit? because isn't charge supposed to be in Coulombs?

Answer 2

Yeah, the question doesnt specify coulombs so much as a magnitude comparison of 25:9.

Answer 3

what is the magnitude of the third charge?

Answer 4

It doesnt want it figured out/known. It's looking for the net forces from 1 and 2 to equal zero on charge 3 when it is placed between them.

Answer 5

\[\huge F={q_1q_2 \over r^2}\]
\[\huge{25qQ \over {(x-0)}^2} ={9qQ \over {(x-2)}^2}\]

Answer 6

something like that, i'm kinda brain dead
I'm not sure that will work, but do you get what I'm trying to do?

Answer 7

Perhaps, let me work it out and compare to the answer. The answer is supposed to be 1.25m

Answer 8

I tried using proportions but I cant figure them out to get 1.25m

Answer 9

i just put it into a calculator
if you solve for x, it comes out to be 1.25 or 5

Answer 10

cross multiply, expand the quadratic, and you have a quadratic equation

Answer 11

the q's all cancel

Answer 12

Yeah, why the x - 0 and x -2 ? Im not sure why you did that part or used this equation actually

Answer 13

ok now that we know it works, let me explain
you agree with coulomb's law that i wrote above right?

Answer 14

Yes

Answer 15

now, i want a location "x" such that the force of some charge Q with q1 is equivalent to that of Q and q2 when i place it in a third location

Answer 16

now, the first side was the 25q and the arbitrary charge Q. the x-0 is saying that there is a distance between the two charges which is necessary for coulomb's law.

Answer 17

the right hand side is the same idea, except x-2 because the two charges q1 and q2 are 2 meters apart

Answer 18

I get it better now. I had to look at it a bit longer I suppose. The x and Q are unknown, but Q's cancel and you're left with determining the distance x from the unknown charge.

Answer 19

Thank you very much for clearing this up for me

Answer 20

no problem