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Specialmias

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## Homework Statement

A meter stick has two charges placed on it at the 0 mark is a charge of +1 coulomb. On the 100cm mark is a charge of +4 coulombs. Where should a proton be placed on the meter stick so that the net force due to both charges is 0.

## Homework Equations

Kc = Coulomb const.

Q= charge

a=unknown distance from +1 on proton

b= unknown distance from +4 on proton

X= proton on line

(Kc*Q1*Qn)/r^2= Force 1 on n

## The Attempt at a Solution

So far I've attempted to do the following:

+1_________________+4

The proton must fall in some region between the two.

If we take 50cm to be the origin of this system and 100 to be +50cm and -50 to be the negative maximum the system at 0 then the +1 charge acts on it towards the negative X direction. So it goes from this:

0________100cm

to

-50cm_______0_______50cm

-[(Kc*Qproton*Q+1)/a^2]+(Kc*Qproton*Q+4)/b^2 = 0

This however, gives me:

[b^2/a^2]=4/1

b/a=2/1

Which to me says that in order for this equation to be true then the distance to the proton on the +4 charge must be twice that of the distance from +1. However I can't seem to find any reasonable way to put this on the meter stick. The only possibility I can think of that would follow this is that the proton must be 30cm from the +1 charge and 60cm from the +4 charge but this still leaves 10cm that don't exist on the meter stick.

Have been working on this for a few hours now and am beginning to think maybe I'm thinking about this the wrong way. Any help is greatly appreciated.