# Plotting electric field lines of a dipole

1. Dec 11, 2011

### silverfox

I was given this equation as the lines of electric fields of a dipole(two opposite charges separated by a finite distance)
e=(1/r^3)*((3cos^2(theta)-1)^2 +sin^2(2theta))^0.5
and I was asked to plot it.
I guess it must be something like this:

but when I try to plot it in wolframalpha.com in polar coords.I dont get the output I expect.
The question is is it the right equation?

2. Dec 11, 2011

### sandy.bridge

Hmm, I also graphed it with wolfram, and it appears to not follow the characteristics of a dipole. It more appears to follow the characteristics of the electric field for like charges, rather than unlike.

3. Dec 11, 2011

### I like Serena

Welcome to PF, silverfox!

I checked what the equation is for an electric dipole and found this:
http://en.wikipedia.org/wiki/Dipole#Field_from_an_electric_dipole

If I work this out in polar coordinates, I get a slightly different formula than the one you have for what appears to be the magnitude of the electric field.
(You can use that $\mathbf{p} = qd\cos\theta \mathbf{\hat r} - qd\sin\theta \hat{\textbf{θ}}$.)
Can it be that you or someone else made a calculation mistake?

Last edited: Dec 11, 2011
4. Dec 21, 2011

### silverfox

I worked a bit more on the problem but I couldn't find an equation myself nor could plot the ones you said or I found on wikipedia...
I was told that if E(r, theta) is the first equation I wrote then E(r, theta, t) would be the same thing times sin(wt) but I dont get it, How does time affect the electric field lines?
And I also thought that p is a border between + and - charges in a dipole which is equal to qd and is a constant value am I wrong?

5. Dec 21, 2011

### I like Serena

In the link I gave you can find an equation for E containing only p and r as variables.
If you substitute the p I gave in my post, you get E(r,θ).
The formula you gave in the OP looks like |E(r,θ)|, but it is not quite right.

It does not have a time dependency.
To make it time dependent, you would need to make the 2 charges time dependent.

p is the vector dipole moment, which is constant.
It is given by p=qd, where -q and +q are the charges, and d is the constant vector from the negative charge to the positive charge.

However, a constant vector is dependent on θ in polar coordinates, since the unit vectors change with θ.