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

  • Thread starter Oijl
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  • #1
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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?

hrw7_22-38.gif



Homework Equations




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?
 

Answers and Replies

  • #2
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.
 
  • #3
rl.bhat
Homework Helper
4,433
7
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.
 
  • #4
I maintain that the y components add. Think of the magnetic field lines of the Earth at the equator.
 

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