What Distance from Charge \( q_1 \) Results in Zero Electric Field?

[craigl34]

Homework Statement

Two particles with positive charges q_1 and q_2 are separated by a distance s.

Along the line connecting the two charges, at what distance from the charge q_1 is the total electric field from the two charges zero?

(Express your answer in terms of some or all of the variables s, q_1, q_2 and K =1/(4*pi*$\epsilon$. If your answer is difficult to enter, consider simplifying it, as it can be made relatively simple with some work.)

Homework Equations

E = K*(q/(d)^2)
E_net = E1 + E2

The Attempt at a Solution

Since both the charges are positive, my E_net = E1 - E2. So I can solve this by finding where E1 and E2 are equal.

Setting the two equations equal I get K(q_1/s^2) = K(q_2/s^2)

Since I'm just concerned with finding the distance from q_1 to the point where the e-field is zero, wouldn't my equation be:

s_1 = (q_1 - (q_2/(s_2)^2)

Since none of the variables are defined, I'm having a hard time figuring out how to choose my 's' (distance). Wouldn't the distance ('s') depend on the magnitude of the charge on q_1 and q_2? How can I show that algebraically without somehow renaming the distance variable something other than 's'?

 

[Tomer]

I'm not sure I understood you.
s is a given distance between the two charges.
You need to find a point between them in which the field is zero - in other words, like you wrote, that E1 = E2.
Let's assume this point has the distance "x" from q1.
What is then the distance of this point from q2? (draw it to yourself if you're having a hard time).

Then use the appropriate formulas to deduce what x should be - in a similar manner to what you've done, but right this time :-)

 

[craigl34]

See I understand that the distance from q_2 would be equal to (total separation 's' - distance from q_2), I just don't know how to represent that with only being able to use the variable 's' representing the total separation.

 

[craigl34]

Nevermind, I figured it out.

I didn't realize that if I put in another variable into the equation 'x = distance from q_1' that it would end up cancelling out during the simplification process.

The answer for me would be:

x = s/1 + sqrt(q_2/q_1)