Electric Field problem :( Is my math wrong or am I doing something else wrong?

Bensky

1. The problem statement, all variables and given/known data
What are the magnitude and direction of the electric field at a point midway between a -7.0 µC and a +6.0 µC charge 5.0 cm apart? Assume no other charges are nearby.

2. Relevant equations

E = KQ_1/r^2 + KQ_2/r^2

3. The attempt at a solution

Q_1 = -7X10^-6 C
Q_2 = 6X10^-6 C
K = 9X10^9
r = 0.025m

E = KQ_1/r^2 + KQ_2/r^2
E = (K)(-7X10^-6)/(.025^2) + (K)(6X10^-6)/(.025^2)
E = -100800000 + 86400000
E = -14400000 N/C or -1.44 X 10^7 N/C (incorrect)

Direction: toward the negative charge (correct)

Doc Al

Careful! You must think through each contribution to the total field in order to give it the proper sign. (You can't just plug into the formula.)

Let's say the negative charge is on the left and the positive charge is on the right. Using what you know about the direction of the field from a point charge, which direction is each field contribution at the point in question? Once you've figured out the direction, then you can give it the proper sign. (For example: To the left = negative; to the right = positive.)

kdv

I am slapping myself now. Of course Doc Al is right. The two E-fields at the center point in the same direction. I erased my post since it was completely wrong.

Bensky

Thanks, I got the answer right, but I'm not sure why I got it right. I ended up making both of them positive and adding them, but from the problem it doesn't seem like the charges would go in the same direction. Why is this so?

kdv

You must ask yourself in what direction the electric field produced by each charge points.

The question is not quite clear because they don't say which charge is on the left and which charge is on the right. Let's pretend the positive charge is on the left and the negative charge is to its right.

Then ask yourself: in what direction is the E field produced by the positive charge at a point midway between the two charges?
In what direction is the E field produced by the negative charge at that point?
Answer those questions and it should clear up why you had to add them up.



Now, to make sure you understand, repeat with this time the positive charge on the right and the negative charge on the left. You will find the the E field points in a different direction but the magnitude of the E field will be the same as before

Doc Al

Looks like kdv gave you a good answer (while I was busy with another thread). Study it and answer his questions step by step.

This fact about charges, which you should know, is key: The field from a positive charge points away from the charge; the field from a negative charge points toward the charge.

Bensky

Thank you to both of you, I understand now.