Finding Potential (Spherical coordinates )

[hadez]

1. . An electric dipole located at the origin in free space has a moment p = 3ax −2ay +az nC·m. Find V at r = 2.5, θ =30◦, φ =40◦.
I find it difficult to solve when its in spherical co-ordinates.2.Relevent Eq
V =P.(r-r')/( 4∏ε|r−r'|²)(|r-r'|)I am confused how to find a unit vector on spherical co-ordinate. ie |r-r'|This que is from william Hayt and page no 100.

 

[vanhees71]

You find the correct potential here:

http://en.wikipedia.org/wiki/Electric_dipole#Potential_and_field_of_an_electric_dipole

Then in your case \vec{r}'=0, because they say it's a dipole at the origin.

 

[hadez]

Thanks for the reply,but my que
1)how to find unit vector in a spherical coordinate system?
2) dipole p is in rectangular coordinate system and distancw vector is in spherical coordinate system.How do i multiply both with a dot product.?
Haunts me.
I spent a whole day and and went mad with vectors buzzin in my brain. I am preparing for an test this fundas are essential.please look into this

 

[rude man]

You can express the observation point for V in cartesian coordinates, then use just the cartesian coordinartes. The observation point is totally defined for you in spherical terms.

V = kp*r/r³

where r is the vector from the origin to the point of observation, and r its magnitude.

So you need to figure out how to express this potential in terms of your cartesian coordinate system, then do the dot-product with the dipole moment expression.

Don't try to do a dot-product in a spherical system. You have to translate to cartesian first.

 

[rude man]

1. . An electric dipole located at the origin in free space has a moment p = 3ax −2ay +az nC·m.

Should say p = 3a i - 2a j + a k,
ijk unit vectors

 

[unscientific]

Should say p = 3a i - 2a j + a k,
ijk unit vectors

yes and do the dot product and expand using $V = \frac{\vec{p} . \vec r}{4 \pi \epsilon_0 r^3}$

And for a dipole centrered at origin along z-axis for example, what can you say about azimuth dependence? Does the potential depend on $\phi$?