# ELECTRIC DIPOLE MOMENT

Two Electric Dipoles denoted by p1 and p2,

p1=2*10^-29 c-m in the direction of z @(x,y,z)=(0,0,0)

p2=2*10^-29 c-m in the direction of y @(x,y,z)=(0,5*10^-10 meters,5*10^-10 meters)

determine potential V @

(x,y,z)=(0,5*10^-10 meters,0)

(x,y,z)=(0,0,5*10^-10 meters)

https://brainmass.com/engineering/electrical-engineering/electric-dipole-moment-288316

## SOLUTION This solution is **FREE** courtesy of BrainMass!

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The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

Note that one can get to the solution without any calculations based on geometry alone. I have solved both explicitly and added the simple solution at the end.

The potential of a dipole at distance r is given by:

(1.1)

Where is the angle between r and p

r is the radius vector from the dipole to the point of observation , while is the vector from the origin to the dipole. Thus:

(1.2)

And the angle can be determined using the dot product:

(1.3)

Hence the potential at due to a dipole located at is:

(1.4)

In our first case we would like to find the potential at from two dipoles. The potential there is the sum of the individual contributions from each dipole.

From the first dipole we obtain:

And from the second dipole:

Thus, the total potential at is:

In the second case, we are asked to find the potential at

From the first dipole we get:

And from the second dipole:

So together the potential at is:

These two results make sense.

In the first case, the observation point is perpendicular and equidistant to both dipoles, hence for both dipoles and they contribute nothing to the potential at that point.

In the second case and the point is equidistant to both dipoles and collinear with the dipole vectors. Only one dipole is pointing to the point while the other points away, which means that the potential contributions will cancel each other out.

https://brainmass.com/engineering/electrical-engineering/electric-dipole-moment-288316