The electric dipole moment (p) of a system is a measure of the separation of positive and negative charges within that system. It's a vector quantity that points from the negative charge to the positive charge. The formula for calculating the electric dipole moment depends on whether you're dealing with a discrete set of charges or a continuous charge distribution.
Discrete Charges:
If you have a system of discrete charges, the electric dipole moment can be calculated using the following formula:
Where:
p is the electric dipole moment vector.
q is the magnitude of the charge.
d is the separation vector between the positive and negative charges.
Continuous Charge Distribution:
For a continuous charge distribution, you need to integrate over the charge distribution to find the electric dipole moment. The formula is:
Where:
p is the electric dipole moment vector.
r is the position vector in space.
ρ(r) is the charge density at the position r.
dV represents an infinitesimal volume element.
The integral integrates over the entire volume of the charge distribution, and for each infinitesimal volume element, the position vector r is dotted with the charge density ρ(r). The result of this integration will give you the total electric dipole moment vector for the continuous charge distribution.
It's important to note that the direction of the electric dipole moment is from the negative charge to the positive charge, regardless of whether you're dealing with a discrete or continuous charge distribution. Also, the unit of electric dipole moment is coulomb-meter (C·m) in the SI system.