Why can't I subtract electric fields from opposite charges directly?

[Himanshu Singh]

Homework Statement

Two charges, one of 3.2 x 10 ^ -9 C, the other one of -6.4x10^-9 C are 42 cm apart. Calculate the net electric field at point P, 15 cm from the postie charge, on the line connecting the charges

(+) -------------(Point)---------------------- (-)
15cm 27cm

Homework Equations

e = kq1/r1^2

The Attempt at a Solution

I know the correct answer, and the steps involved as well (answer is 1.3 x 10^3 N/C to the right) but I don't get why they do it the way they do it. Can't you just use e = kq1/r1^2 with q being 3.2 x 10 ^ -9 C and d being 0.42m and then subtract that from kq1/r1^2 with q being 3.2 x 10 ^ -9 C and d being 0.27m? I always get the wrong answer with it.

 

[BvU]

Write out the steps for the two paths in detail and see where you go astray. Post both if you still don't see it.

 

[Chandra Prayaga]

Write out the steps for the two paths in detail and see where you go astray. Post both if you still don't see it.

Also draw the arrows in the diagram showing the fields that you want to calculate.

 

[TachyonLord]

The Attempt at a Solution

I know the correct answer, and the steps involved as well (answer is 1.3 x 10^3 N/C to the right) but I don't get why they do it the way they do it. Can't you just use e = kq1/r1^2 with q being 3.2 x 10 ^ -9 C and d being 0.42m and then subtract that from kq1/r1^2 with q being 3.2 x 10 ^ -9 C and d being 0.27m? I always get the wrong answer with it.

Well, the problem is that, the Electric field is a vector and therefore, the net electric field at a point will be the resultant of the electric fields "caused" by both the charges q1 and q2. You are ignoring the other charged particle (q2 = -6.4x10^-9C). As a result you miss out on the contribution due to q2 and get the wrong answer. Account for the both charges and let me know if you get the answer. Do reply if you didn't get this.

 

[RPinPA]

and then subtract that from kq1/r1^2 with q being 3.2 x 10 ^ -9 C and d being 0.27m?

Since you used the distance from the negative charge, I assume you are referring here to the negative charge and you just typed in the wrong number.

But I think what you're missing is fact that electric field is a vector and you have to take into account the direction of the field.

What direction is the field from a positive charge? What direction is it pointing at point P, right or left?
What direction is the field from a negative charge? What direction is it pointing at point P, right or left?