Method of images
From Wikipedia, the free encyclopedia
Method of images (or mirror images) is used in electrostatics (magnetostatics) to simply calculate or visualize the distribution of the electric (magnetic) field of a charge (magnet) in a vicinity to the conducting (superconducting) surface. It is based on the fact that the tangential (normal) component of the electrical (magnetic) field to the surface of a conductor (superconductor) is zero, and that some field E with rot E = 0 and div E = 0 in some region is uniquely defined by its normal component over the surface which confines this region (the uniqueness theorem).
A textbook example is an infinitely flat conducting surface (see Fig. 1). In this case the field distribution between the surface and a charge is the same as between this charge and another charge (imaginary charge), which is the mirror image of the real charge in respect to the surface but has the opposite sign. Evidently, in case of an electrical dipole, the vector of the mirrored dipole will have the opposite sign. Therefore, the force between the electrical charge or system of charges and the conducting surface is attractive. See also Method of image charges.
In case of magnet-superconductor pair (the superconductor here is ideal, to which the magnetic field does not penetrate), the mirror image of the magnet will have a magnetization vector which is mirrored but of the same sign (see Fig. 2). This can be thought as due to additional sign change upon mirroring of an axial vector which the magnetization is. The force between the magnet and the superconducting surface is therefore repulsive.
[edit] Further reading
- Feynman, Richard; Leighton, Robert; Sands, Matthew (1989). Feynman Lectures on Physics, Mainly Electromagnetism and Matter. Addison-Wesley. ISBN 0-201-51003-0.
