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A key point is that the potential of the dipole falls off faster with distance R than that of the point charge. The electric field of the dipole is the negative gradient of the potential, leading to: [ 7 ] E ( R ) = 3 ( p ⋅ R ^ ) R ^ − p 4 π ε 0 R 3 . {\displaystyle \mathbf {E} \left(\mathbf {R} \right)={\frac {3\left(\mathbf {p} \cdot ...
A theoretical magnetic point dipole has a magnetic field of exactly the same form as the electric field of an electric point dipole. A very small current-carrying loop is approximately a magnetic point dipole; the magnetic dipole moment of such a loop is the product of the current flowing in the loop and the (vector) area of the loop.
Each term in the expansion is associated with a characteristic moment and a potential having a characteristic rate of decrease with distance r from the source. Monopole moments have a 1/r rate of decrease, dipole moments have a 1/r 2 rate, quadrupole moments have a 1/r 3 rate, and so on. The higher the order, the faster the potential drops off.
Thus a double layer potential u(x) is a scalar-valued function of x ∈ R 3 given by = | | where ρ denotes the dipole distribution, ∂/∂ν denotes the directional derivative in the direction of the outward unit normal in the y variable, and dσ is the surface measure on S.
The electric potential at any location, r, in a system of point charges is equal to the sum of the individual electric potentials due to every point charge in the system. This fact simplifies calculations significantly, because addition of potential (scalar) fields is much easier than addition of the electric (vector) fields.
Magnetic dipole–dipole interaction, also called dipolar coupling, refers to the direct interaction between two magnetic dipoles. Roughly speaking, the magnetic field of a dipole goes as the inverse cube of the distance, and the force of its magnetic field on another dipole goes as the first derivative of the magnetic field. It follows that ...
In the case of two classical point charges, + and , with a displacement vector, , pointing from the negative charge to the positive charge, the electric dipole moment is given by =. In the presence of an electric field , such as that due to an electromagnetic wave, the two charges will experience a force in opposite directions, leading to a net ...
In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field. The magnetic dipole moment of an object determines the magnitude of torque the object experiences in a given magnetic field. When the same magnetic field is applied ...