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As such, they are often written as E(x, y, z, t) (electric field) and B(x, y, z, t) (magnetic field). If only the electric field (E) is non-zero, and is constant in time, the field is said to be an electrostatic field. Similarly, if only the magnetic field (B) is non-zero and is constant in time, the field is said to be a magnetostatic field.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
Similarly, if only the magnetic field (B) is non-zero and is constant in time, the field is said to be a magnetostatic field. However, if either the electric or magnetic field has a time-dependence, then both fields must be considered together as a coupled electromagnetic field using Maxwell's equations. [9]
The electric field (E) is the dual of the magnetic field (H). The electric displacement field (D) is the dual of the magnetic flux density (B). Faraday's law of induction is the dual of Ampère's circuital law. Gauss's law for electric field is the dual of Gauss's law for magnetism. The electric potential is the dual of the magnetic potential.
The magnetic field of permanent magnets can be quite complicated, especially near the magnet. The magnetic field of a small [note 6] straight magnet is proportional to the magnet's strength (called its magnetic dipole moment m). The equations are non-trivial and depend on the distance from the magnet and the orientation of the magnet.
Electromagnets often use a wire curled up into solenoid around an iron core which strengthens the magnetic field produced because the iron core becomes magnetised. [15] [16] Maxwell's extension to the law states that a time-varying electric field can also generate a magnetic field. [12]
Magnetic field (green) induced by a current-carrying wire winding (red) in a magnetic circuit consisting of an iron core C forming a closed loop with two air gaps G in it. In an analogy to an electric circuit, the winding acts analogously to an electric battery, providing the magnetizing field , the core pieces act like wires, and the gaps G act like resistors.
The magnetic field (B, green) is directed down through the plate. The Lorentz force of the magnetic field on the electrons in the metal induces a sideways current under the magnet. The magnetic field, acting on the sideways moving electrons, creates a Lorentz force opposite to the velocity of the sheet, which acts as a drag force on the sheet.