The electric field at a midpoint of two charges

[marrone]

Problem 1:

Homework Statement

What is the electric field at a point midway between a -8.64uC and 6.97uC charge 7.63 cm apart? Take the direction towards the positive charge to be positive and assume no other charges nearby.

Homework Equations

E=kQ/r²

The Attempt at a Solution

So what I've been doing is finding the strengths of the electric fields for each charge at the midpoint, which is .03185 m, and then adding them together.

e.g. E₁=k(6.97*10^-6)/(.03185²)

E₂=k(-8.64*10^-6)/(.03185²)

I get -1.48*10⁷, when the answer ought to be -9.56*10⁷

What am I doing wrong?

 

[Redbelly98]

I haven't checked your numbers thoroughly, but:

Have you thought carefully about the direction the field from each charge should point?

Also, try again on 7.63/2 cm = ____ m?

 

[ice ace]

I think the problem is how you add the numbers together. Since the test charge placed in middle is positive, the negative charge will try to attract it and and positive charge will repel it. When you add the two values of E together as you did, you are cancelling the effect of the negative charge with the positive charge, which is not true as both E₁ and E₂ makes the test charge go more to the negative charge. So simply, make E₂ value negative and add to E₁.

 

[marrone]

Well, what I had been doing is making E2 negative and adding it to a positive E1, but thinking about what redbelly said, a field will always point from positive to negative, which is in a negative direction. So I made both of them negative and added them together, and I got the right answer.

Oh, and thanks for checking the value of the midpoint. I didn't see I had mixed up the digits after the decimal point.