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The above form for the Poynting vector represents the instantaneous power flow due to instantaneous electric and magnetic fields. More commonly, problems in electromagnetics are solved in terms of sinusoidally varying fields at a specified frequency. The results can then be applied more generally, for instance, by representing incoherent ...
Power is the rate with respect to time at which work is done; it is the time derivative of work: =, where P is power, W is work, and t is time.. We will now show that the mechanical power generated by a force F on a body moving at the velocity v can be expressed as the product: = =
[1]: 3 The portion of instantaneous power that results in no net transfer of energy but instead oscillates between the source and load in each cycle due to stored energy is known as instantaneous reactive power, and its amplitude is the absolute value of reactive power.
A differential equation of motion, usually identified as some physical law (for example, F = ma), and applying definitions of physical quantities, is used to set up an equation to solve a kinematics problem. Solving the differential equation will lead to a general solution with arbitrary constants, the arbitrariness corresponding to a set of ...
[10] [11] Moreover, words which are synonymous in everyday speech are not so in physics: force is not the same as power or pressure, for example, and mass has a different meaning than weight. [12] [13]: 150 The physics concept of force makes quantitative the everyday idea of a push or a pull. Forces in Newtonian mechanics are often due to ...
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).
This also means the constraint forces do not add to the instantaneous power.) The time integral of this scalar equation yields work from the instantaneous power, and kinetic energy from the scalar product of acceleration with velocity. The fact that the work–energy principle eliminates the constraint forces underlies Lagrangian mechanics. [28]
Action principles are "integral" approaches rather than the "differential" approach of Newtonian mechanics.[2]: 162 The core ideas are based on energy, paths, an energy function called the Lagrangian along paths, and selection of a path according to the "action", a continuous sum or integral of the Lagrangian along the path.