Electric Field due to a Dipole (not on a z-axis)

[Oijl]

Homework Statement

The figure shows an electric dipole. What is the magnitude of the dipole's electric field at point P, located at distance r >> d?

Homework Equations

The Attempt at a Solution

I suppose I could define the angle with which I could write Ey = Esin\theta, but this problem is a webassign.com problem, so it's online and I can't define anything.

The magnitude of the electric field at p due to the dipole would be very small, and I first estimated it to be zero (since the problem asks for an estimation anyway).

Without defining and using a theta, how could I represent the magnitude of the electric field?

 

[loveequation]

Just introduce theta temporarily. It goes away in the end since you know what it is.

The electric field vectors of the two charges add in the y direction and cancel in the x direction. Hence
<br /> |\vec E| = |E_y| = (2 q/R) \sin(\theta)<br />
where I will let you write down R and \sin(\theta) in terms of r and d.

The rest you can do.

 

[rl.bhat]

Just introduce theta temporarily. It goes away in the end since you know what it is.

The electric field vectors of the two charges add in the y direction and cancel in the x direction. Hence
<br /> |\vec E| = |E_y| = (2 q/R) \sin(\theta)<br />
where I will let you write down R and \sin(\theta) in terms of r and d.

The rest you can do.

In the dipole one is +ve charge and the other -ve charge.
The electric field E = 1/4πε_ο*q/[r² + (d/2)²]
Their y-components cancel out and x-components add.

 

[loveequation]

I maintain that the y components add. Think of the magnetic field lines of the Earth at the equator.