# An Electrostatics Problem - Eletric Field

## Homework Statement

Question 2.2
http://www.studyjapan.go.jp/en/toj/pdf/08-007.pdf
The picture is in the next page of the problem.

• k is the Coulomb constant.
• q+ is the charge at point A.
• q- is the charge at point B.
• AC = BC = CD = a

E = kq/d²
a² = b² + c²

## The Attempt at a Solution

I put the vectors on the force line at AD and DB, adding the vectors we get the eletric field at point D, the problem is that when I use a² = b² + c² (observe that is a right triangle) I get the result Kq/a, answer D, but the correct answer is B. Where is wrong?

I have just learned Electrostatics, maybe it is a simple problem, but I can not solve.

Thank you.

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tiny-tim
Homework Helper
Welcome to PF!

Hi Yukimi! Welcome to PF! I put the vectors on the force line at AD and DB, adding the vectors we get the eletric field at point D, the problem is that when I use a² = b² + c² (observe that is a right triangle) I get the result Kq/a, answer D, but the correct answer is B. Where is wrong?
Show us how you got Kq/a. As I said, I got by doing the addition of the vectors from A to D (force line from charge q+) and from D to B (force line from charge q-), I did that because the final vector will be the electric field at point D (Ed), using the pythagorean theorem (it is a right triangle, because DC and AB are perpendicular) I got AD = AB = a times square root of 2, using the pythagorean theorem one more time I got Ed = Kq/a.

tiny-tim
Homework Helper
I don't understand how you avoided getting a square on the bottom. Sorry, I don't understand, are you saying about the equation using the pythagorean theorem? If that is the case, here is how I did:

(kq/a*root 2)² + (kq/a*root 2)² = Ed²
2[(kq)²/2a²] = Ed²
kq/a = Ed

gneill
Mentor
Ah. The magnitude of the field strength for a charge at distance a√2 is

E = k*q/(a√2)2 = k*q/(2a2)

That's the magnitude of the field due to one charge. Resolve this into components via geometry for both of the charge sources. Add the like components to find the net field.

tiny-tim
Homework Helper
(kq/(a*root 2)²)² + (kq/(a*root 2)²)² = Ed² 