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In the electric and magnetic field formulation there are four equations that determine the fields for given charge and current distribution. A separate law of nature, the Lorentz force law, describes how the electric and magnetic fields act on charged particles and currents. By convention, a version of this law in the original equations by ...
Position vector r is a point to calculate the electric field; r′ is a point in the charged object. Contrary to the strong analogy between (classical) gravitation and electrostatics, there are no "centre of charge" or "centre of electrostatic attraction" analogues. [citation needed] Electric transport
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.
Interface conditions describe the behaviour of electromagnetic fields; electric field, electric displacement field, and the magnetic field at the interface of two materials. The differential forms of these equations require that there is always an open neighbourhood around the point to which they are applied, otherwise the vector fields and H ...
The electric field is perpendicular, locally, to the equipotential surface of the conductor, and zero inside; its flux πa 2 ·E, by Gauss's law equals πa 2 ·σ/ε 0. Thus, σ = ε 0 E . In problems involving conductors set at known potentials, the potential away from them is obtained by solving Laplace's equation , either analytically or ...
[10]: 24, 90–91 This implies there are two kinds of electric fields: electrostatic fields and fields arising from time-varying magnetic fields. [ 10 ] : 305–307 While the curl-free nature of the static electric field allows for a simpler treatment using electrostatics, time-varying magnetic fields are generally treated as a component of a ...
All of the time derivatives vanish from the equations, leaving two expressions that involve the electric field, = and =, along with two formulae that involve the magnetic field: = and =. These expressions are the basic equations of electrostatics , which focuses on situations where electrical charges do not move, and magnetostatics , the ...
where the conductivity σ and resistivity ρ are rank-2 tensors, and electric field E and current density J are vectors. These tensors can be represented by 3×3 matrices, the vectors with 3×1 matrices, with matrix multiplication used on the right side of these equations.