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Poynting vector in a static field, where E is the electric field, H the magnetic field, and S the Poynting vector. The consideration of the Poynting vector in static fields shows the relativistic nature of the Maxwell equations and allows a better understanding of the magnetic component of the Lorentz force, q(v × B).
The members of the algebra may be decomposed by grade (as in the formalism of differential forms) and the (geometric) product of a vector with a k-vector decomposes into a (k − 1)-vector and a (k + 1)-vector. The (k − 1)-vector component can be identified with the inner product and the (k + 1)-vector component with the outer product. It is ...
where: is the rate of change of the energy density in the volume. ∇•S is the energy flow out of the volume, given by the divergence of the Poynting vector S. J•E is the rate at which the fields do work on charges in the volume (J is the current density corresponding to the motion of charge, E is the electric field, and • is the dot product).
The Poynting vector = represents the direction and magnitude of the power flow in the electromagnetic field (the length of the vectors shown here are not to scale; only the direction is being shown) In the region of space around the battery, the Poynting vectors are directed outward, indicating that power flows out from the battery into the ...
All but the last term of can be written as the tensor divergence of the Maxwell stress tensor, giving: = +, As in the Poynting's theorem, the second term on the right side of the above equation can be interpreted as the time derivative of the EM field's momentum density, while the first term is the time derivative of the momentum density for ...
Also calculating power flow direction (Poynting vector), a waveguide's normal modes, media-generated wave dispersion, and scattering can be computed from the E and H fields. CEM models may or may not assume symmetry, simplifying real world structures to idealized cylinders, spheres, and other regular geometrical objects. CEM models extensively ...
In the tensor calculus formulation, the electromagnetic tensor F αβ is an antisymmetric covariant order 2 tensor; the four-potential, A α, is a covariant vector; the current, J α, is a vector; the square brackets, [ ], denote antisymmetrization of indices; ∂ α is the partial derivative with respect to the coordinate, x α.
So, dimensionally, the Poynting vector is S = power / area = rate of doing work / area = ΔF / Δt Δx / area , which is the speed of light, c = Δx / Δt, times pressure, ΔF / area.