Strange question with 2 charges, and net electric field between them = 0

1. Feb 3, 2005

michaelw

Two charges, –16 and +4.0 mC, are fixed in place and separated by 3.0 m. (a) At what spot along a line through the charges is the net electric field zero? Locate this spot relative to the positive charge. (b) What would be the force on a charge of +14 mC placed at this spot?

I am totally flabbergasted by this question
Our prof doesnt really give many formulas, or any at all, as we generally have to figure out what to use and when

But in this case, what formula would you use to even get started?

2. Feb 3, 2005

gnome

For A, what is the equation for and electric field E due to a point charge q at a distance r from the charge? What is the direction of the field?

That's all you need, plus some algebra.

For B, no formula at all, just some thought.

3. Feb 3, 2005

MathStudent

the E set up by a point charge q at a distance of r is
$$\vec{E} = \frac{kq}{r^2}$$

the $\vec{E}$ points away from q if q is positive, and towards q if q is negative

4. Feb 3, 2005

vaxopy

wow im confused
and this is simple too..

charge 1 points to the 'left' (assume left is where the -16mC charge is)
charge 2 points to right

so you set
E1 = E2

but how do you isolate r^2 now? you end up with
value/r^2 = value/r^2..

if you multiply both sides by r^2, they cancel.. clearly im missing something elementary

5. Feb 4, 2005

MathStudent

what do you mean charge 1 points to the left? The electric field set up by a negative point charge points toward the charge, but this is relative to where your evaluating the electric field from. Conversely, the electric field set up by a positive point charge points radially away from the charge

First try to figure out where the the point must be located relative to the two point charges.

-------------(-16mC)---------------(+4mC)---------------->x
$$.\ \ \ \ \ \ \ \ \ \ a \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ b \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ c$$

as you see the digram sets up three intervals as to where the point might be where the E = 0.

edit: the letters above just indicate the three seperate intervals, and do not represent length

Last edited: Feb 4, 2005
6. Feb 4, 2005

michaelw

heres what i did..
(8.99*10^9)(4*10^-6)/m^2 = (8.99*10^9)(16*10^-6)/(m+3)^2
m is the distance between 4uC and x

i then got
((3+m)^2)/(m^2) = 4*10^-6

am i on the right track? how can i solve for m now? (i dont have a graphing calculator)

7. Feb 4, 2005

MathStudent

Equation looks good!
I just want to mention something about the charges though. Just so you know mC represents millicoulombs (10^-3 C), and $\mu C$ represents microcoulombs (10^-6 C). Did the question give the charges in mC or $\mu C$? If its supposed to be millicoulombs, then your charges are wrong.

LHS looks good, but what is (16*10^-6 / 4*10^-6), its not 4*10^-6.

You don't need a graphing calculator to solve this, just a little algebra.

Last edited: Feb 4, 2005