# Calculating Where Electric Field Between Two Charges is equal to Zero

#### Brodo17

Two carges of + 1.5 x 10 ^-6 C and + 3.0 X 10^-6 C are .20m apart. Where is the electric field between them equal to zero?

Do I use the equation Kq2/r^2 ? I also have Kq1q2 / r^2
I am pretty sure the problem can be solved using those two equations, and most likely the first equation

Im sorry but I really dont know how to figure this out. I tried to somehow figure it out by finding how much force the first charge is exerting on the second, and vice versa and then subtracting the smaller force from the larger. I dont see how that helps me though.
This question is not for marks, I just really need to learn how to do it today for my test tommorow. Please Help!

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#### Cyosis

Homework Helper
The first formula is the electric field strenghty of q2 at a distance r. What you want to solve is $E_1+E_2=0$. Can you find expressions for $E_1, E_2$?

Edit: made a pretty big "braino"

Last edited:

#### tiny-tim

Homework Helper
Hi Brodo17! (try using the X2 and X2 tags just above the Reply box )
Two carges of + 1.5 x 10 ^-6 C and + 3.0 X 10^-6 C are .20m apart. Where is the electric field between them equal to zero?

Do I use the equation Kq2/r^2 ? I also have Kq1q2 / r^2
Kq2/r22 is the field at distance r2 from charge #2.

Kq1q2/r2 is the force of charge #2 on charge #1 (and vice versa).

You need to use the first equation, twice, with r1 and r2 #### Brodo17

I dont understand! Could someone please solve the problem and show me the solution.

#### tiny-tim

Homework Helper
Hi Brodo17! Thanks for the PM! Brodo17 said:
Thanks for replying to my forum, however if you understand how to get the answer could you show exactly how to do it.
It isnt for marks
Sorry, but you have to make an effort yourself …

what are the two equations you get for r1 and r2 ? #### diazona

Homework Helper
Look at what tiny-tim said a couple of posts back. The electric field at a distance r from a charge q is
$$E = K \frac{q}{r^2}$$
(Also remember the direction: the electric field of a positive charge points away from the charge) Pick a point between the two charges - say, at a distance r1 from charge #1 - and calculate the electric field produced by charge #1 at that point. Then calculate the electric field produced by charge #2 at that point. The total electric field at that point is the sum of those two electric fields (but do remember to take direction into account! If the fields point in opposite directions, they subtract, instead of adding)

#### Brodo17

ok so I pick a random point and calculate the force each charge is exerting at that point? I really dont understand where to go from there though.

#### LowlyPion

Homework Helper
ok so I pick a random point and calculate the force each charge is exerting at that point? I really dont understand where to go from there though.
Not exactly.

The charges are a fixed distance apart. That means that the sum of the distance to each must add to that distance.

The force from each - in opposite directions must be equal ... so, construct an equation for the magnitude of the force of 1 is equal to the force from the other. Then exploit the total distance relationship ... then solve.

#### skoks

Is it okay to get this thread started up again I have the same question and similar difficulties....

Even if I do as you said, and use E=E1+E2, I still have the problem of having either the two variables of r, or no variable i'm so confused.

If I solve for values of E at a specific point and do vector addition I still don't know when they equal to zero...?

#### skoks

Its okay, i figured it out. I'm an idiot....