Solving for Electric Field Strength

[bikeeich]

Homework Statement

An electric dipole is formed from

1.0 nC charges spaced 2.4 mm apart. The dipole is at the origin, oriented along they-axis. What is the electric field strength at the following points?
a. (x, y) = (10 cm, 0 cm)
b. (x, y) = (0 cm, 10 cm)

Homework Equations

Pythagorean Theorem a^2 + b^2 = C^2
F= (kq1q2)/r^2

The Attempt at a Solution

I solved for r^2 using the Pythagorean theorem and I got it to equal 0.01 m. Plugging r into the Force equation I got 900N. I think for part a I need to use vectors of the angle created between the x-axis and the hypotenuse (r) but I am not sure how to use that to get the electric field strength.

 

[mfb]

F= (kq1q2)/r^2 is a formula for forces between point charges, and it does not take the direction into account.

Do you have a formula for the electric field of a dipole?
If not, do you have a formula for the force between two charges in vector form?

 

[bikeeich]

Is it E= (qd)/kz^3
if d = the distance between the charges and z is the distance I to the point I am solving for?

 

[mfb]

How did k go to the denominator (which needs brackets)? It is the right direction, but that formula needs more vectors to make sense.

 

[bikeeich]

So if the formula is F = (kqd)/z^3,
I plug in and get [(9.0E9 Nm^2/C^2)*(1.0E-9C)*(2.4E-3m)]/(0.01m)^3 = 21600 N/C
Is that all I have to do to solve for the x-axis values? and how does this equation relate to part b where both charges are no longer an equal distance to the point on they y-axis?