EFeldKomponenten

EFeldKomponenten refers to the components of the electric field vector E in a chosen coordinate system. The electric field is a vector field E(r, t) defined at each point in space. In Cartesian coordinates, E has three components Ex, Ey, Ez, such that E = Ex x_hat + Ey y_hat + Ez z_hat. More generally E = sum over i of E_i e_i where e_i are the basis vectors. The components are obtained by projecting the field onto the basis: Ex = E · x_hat, Ey = E · y_hat, Ez = E · z_hat. The magnitude is |E| = sqrt(Ex^2 + Ey^2 + Ez^2).

In electrostatics with a potential V, E is conservative and E = -grad V; this yields Ex = -∂V/∂x, Ey = -∂V/∂y, Ez = -∂V/∂z. Units for the components are volts per meter (V/m) or newtons per coulomb (N/C). The components determine the field’s direction and strength locally, and together they describe field lines and equipotential surfaces.

Under a change of coordinates, the components transform according to the coordinate transformation; the vector itself is invariant though the numerical components change. In non-orthonormal or curvilinear bases, the components require the metric coefficients and can be covariant or contravariant.

Applications include solving Maxwell’s equations and boundary-value problems, where the divergence div E = ρ/ε0 and curl E = -∂B/∂t relate to the components. Boundary conditions specify normal and tangential components across interfaces. A simple example is the field of a point charge q: E(r) = (1/(4π ε0)) q r_hat / r^2, with components Ex = (1/(4π ε0)) q x / r^3, Ey = (1/(4π ε0)) q y / r^3, Ez = (1/(4π ε0)) q z / r^3.