Electricity And Magnetism

Berkeley Physics Course Tomo 2 - Electricidad y Magnetismo by Edward M. Purcell.

By Edward M. Purcell.

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Both particles have velocities close to that of light, or 2. the electrostatic component of the force is cancelled by the electrostatic force of an equal and opposite stationary charge. The latter is just what happens when electrons are moving along conducting wires because those contain equal numbers of fixed positive charges. Although the electrons move at velocities much less than that of light, there are enormous numbers of them, so useful forces are produced. That is why magnetic forces can be used to generate electric power and to drive electric motors.

In large three-dimensional problems the number of variables can be very large indeed and the computation time correspondingly long. Very often the result required from a field calculation is not the detailed field information but only a single number such as the capacitance. For problems of this kind an alternative method, the boundary element method, is useful because it only requires mesh points and potentials to be specified on the boundaries. This has the benefit that the number of variables in the solution is less than in the corresponding finite difference or finite element solution by two or three orders of magnitude.

7 Calculation of resistance by energy methods It has already been observed that capacitances can be calculated by energy methods to an accuracy which is adequate for many purposes. Similar methods can be used to calculate resistances. In this case it is assumed that the effect of perturbing the distribution of the electric field and the current density from equilibrium is to increase the rate of energy dissipation. 19) giving an upper bound for the resistance. 20) giving a lower bound for R. 8 Summary In this chapter we have explored the links between the theory of electromagnetism and the theory of electric circuits.

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