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Field lines of a point dipole of any type, electric, magnetic, acoustic, etc. A physical dipole consists of two equal and opposite point charges: in the literal sense, two poles. Its field at large distances (i.e., distances large in comparison to the separation of the poles) depends almost entirely on the dipole moment as defined above.
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 ...
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.
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 ...
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.
It follows that the dipole-dipole interaction goes as the inverse fourth power of the distance. Suppose m 1 and m 2 are two magnetic dipole moments that are far enough apart that they can be treated as point dipoles in calculating their interaction energy. The potential energy H of the interaction is then given by:
Referring to the figure, we wish to find the potential inside a grounded sphere of radius R, centered at the origin, due to a point charge inside the sphere at position (For the opposite case, the potential outside a sphere due to a charge outside the sphere, the method is applied in a similar way). In the figure, this is represented by the ...
The potential V(R), due to the charge distribution, at a point R outside the charge distribution, i.e., | R | > r max, can be expanded in powers of 1/R. Two ways of making this expansion can be found in the literature: The first is a Taylor series in the Cartesian coordinates x , y , and z , while the second is in terms of spherical harmonics ...