Question

Need help solving this equation...
(k * Q1 * Q)/(x^2) = (k * 4Q1 * Q)/(L-x^2)

Answer 1

Q1 and Q are constant, so is k. Variables are L and x.

Answer 2

Right, you should cancel them off from both sides.

Answer 3

so right off the bat I can cancel all of those and will be left with....

1/x^2 = 4 / (L-x)^2 This was supposed to be (L-x)^2 in problem description.

Answer 4

right?

Answer 5

Hi :)

Cross multiply!

Answer 6

Hi,
so then I will have...

4x^2 = (L-x)^2

Answer 7

Correct! There's no way to solve this equation until you're specified anything else.

Answer 8

then I can expand (L-x)^2 to L^2 -2Lx + x^2

Answer 9

Yes, very much!

Answer 10

how about L = x + ( L -x) ?

Answer 11

Right! But can you explain how'll use this further?

Answer 12

No. My book has a solution for this....I have been messing with this for awhile and agree with you that there is no way to solve it wihtout something I am missing. Ill carefully look at the problem again.

Answer 13

Can you write what your book says here?

Answer 14

Two charges -Q1 and -4Q1 are a distance L apart. These 2 charges are free to move but do not because a third charge holds the two in equilibrium. What must be the magnitude and placement of the third charge?

Answer 15

Hey wait! I think the question was changed

Answer 16

Oh alright! Principle of superposition!

Answer 17

Yes Thats where the equations I was working with came from.

Answer 18

Thats not (L - x)^2 but L-x^2 right?

Answer 19

In that case I think its better

Answer 20

It should be (L-x)^2

Answer 21

Oh ok. Ive got a little rusty at my electrostatics.

Answer 22

I think you should ask this in physics! Those folks are good at this

Answer 23

Its just a math problem at this point.

Answer 24

I understand what you mean

Answer 25

Aravind any inputs?

Answer 26

One thing we can directly say is that the third charge is positive.

(k * Q1 * Q)/(x^2) = (k * 4Q1 * Q)/(L-x)^2

Answer 27

You can cancel k*Q*Q1 on both sides. Then take square root :)

Answer 28

How could it be so simple lol.............so could you have solved it if you cross multiplied and kept going that route?

Answer 29

Why go the complicated way when you can do it in the simple way? Yes ultimately in any method we get the same answer.

Answer 30

Oh yes I forgot about the square root! That was very stupid lol

Answer 31

Yes all the terms come in a way that compels us to take the root. 4,x^2,(l-x)^2

Answer 32

Thank you!