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

by Oijl
Tags: dipole, electric, field, zaxis
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Oijl
#1
Sep6-09, 11:08 PM
P: 115
1. The problem statement, all variables and given/known data
The figure shows an electric dipole. What is the magnitude of the dipole's electric field at point P, located at distance r >> d?




2. Relevant equations


3. The attempt at a solution

I suppose I could define the angle with which I could write Ey = Esin[tex]\theta[/tex], 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?
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loveequation
#2
Sep7-09, 02:27 AM
P: 39
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 [itex]y[/itex] direction and cancel in the [itex]x[/itex] direction. Hence
[tex]
|\vec E| = |E_y| = (2 q/R) \sin(\theta)
[/tex]
where I will let you write down [itex]R[/itex] and [itex]\sin(\theta)[/itex] in terms of [itex]r[/itex] and [itex]d[/itex].

The rest you can do.
rl.bhat
#3
Sep7-09, 09:02 AM
HW Helper
P: 4,433
Quote Quote by loveequation View Post
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 [itex]y[/itex] direction and cancel in the [itex]x[/itex] direction. Hence
[tex]
|\vec E| = |E_y| = (2 q/R) \sin(\theta)
[/tex]
where I will let you write down [itex]R[/itex] and [itex]\sin(\theta)[/itex] in terms of [itex]r[/itex] and [itex]d[/itex].

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

loveequation
#4
Sep7-09, 02:17 PM
P: 39
Electric Field due to a Dipole (not on a z-axis)

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


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