By J. E. Parton, S. J. T. Owen, M. S. Raven (auth.)
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Extra resources for Applied Electromagnetics
The fteld has cylindrical symmetry. 3 Field due to a surface charge Ps coulombs/m 2 The electric fteld strength at any point P due to such a surface S may be found by integration E= J surface Ps dS A_ 2 a, "f'T(;e 0 r where a, is a unit vector along r, the position vector of P with respect to dS. If we have a choice of axes these can be ftxed so that the charged surface lies in the yz plane. The point P can be on the x axis, that is coordinates (a, 0, 0). 5b. 5 (a) Surface in yz plane. (b) Infinitely long plane.
When there is a distribution of charge pv(x, y, z), which will vary with position in the volume considered total stored energy WE =! JPv V d(vol) vol 39 THE ELECTRIC FIELD We can now re-interpret this stored energy in terms of the electric displacement and electric field strength rather than in terms of charge and potential. 10 Energy density in an electric field Starting from the above expression for the stored energy of a charge distribution WE=! f pyV d(vol) vol for the charge system, we replace p v = div D = V.
13, and its axis when rotating with maximum velocity would give the direction of curl. 13 Illustration of cur/. fieldS by means of its gradient or else the line integral around a closed path in the corresponding vector field would have been zero. Although curl suggests that motion or flow in curves is present this is not strictly necessary, as in the example quoted. A field in which the curl is zero is generally called irrotational and by defmition is also lamellar since 1F. dJ = 0. In general a conservative field is both irrotational and lamellar but by common usage the former term has now almost entirely replaced the latter.
Applied Electromagnetics by J. E. Parton, S. J. T. Owen, M. S. Raven (auth.)