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The term "Maxwell's equations" is often also used for equivalent alternative formulations. Versions of Maxwell's equations based on the electric and magnetic scalar potentials are preferred for explicitly solving the equations as a boundary value problem, analytical mechanics, or for use in quantum mechanics.
Solar-powered calculators are hand-held electronic calculators powered by solar cells mounted on the device. [1] They were introduced at the end of the 1970s. [2]Amorphous silicon has been used as a photovoltaic solar cell material for devices which require very little power, such as pocket calculators, because their lower performance compared to conventional crystalline silicon solar cells is ...
Electromagnetic behavior is governed by Maxwell's equations, and all parasitic extraction requires solving some form of Maxwell's equations. That form may be a simple analytic parallel plate capacitance equation or may involve a full numerical solution for a complex 3D geometry with wave propagation.
In fact, Maxwell's equations were crucial in the historical development of special relativity. However, in the usual formulation of Maxwell's equations, their consistency with special relativity is not obvious; it can only be proven by a laborious calculation. For example, consider a conductor moving in the field of a magnet. [8]
Position vectors r and r′ used in the calculation. The starting point is Maxwell's equations in the potential formulation using the Lorenz gauge: =, = where φ(r, t) is the electric potential and A(r, t) is the magnetic vector potential, for an arbitrary source of charge density ρ(r, t) and current density J(r, t), and is the D'Alembert operator. [2]
The inhomogeneous Maxwell equation leads to the continuity equation: =, = implying conservation of charge. Maxwell's laws above can be generalised to curved spacetime by simply replacing partial derivatives with covariant derivatives:
What is charge density in electrostatics becomes proper charge density [5] [6] [7] and generates a magnetic field for a moving observer. A revival of interest in this method for education and training of electrical and electronics engineers broke out in the 1960s after Richard Feynman 's textbook. [ 8 ]
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 ...