Applied Electromagnetics by J. E. Parton, S. J. T. Owen, M. S. Raven (auth.)

By J. E. Parton, S. J. T. Owen, M. S. Raven (auth.)

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If the reference point B is at infinity we can take r 8 ~ oo and assume VB = 0. _volts 47t€o r A Similarly for any other point C the potential Vc is (Q/4rre 0 )(1/rc) and V AC = VA - Vc = (Q/4rre 0 )(1/rA - 1/rc). 3 Potential due to other charge distributions It is now possible to consider the potential produced at a point by various types of charge distributions, and examples are given of four simple distributions. (i) A system of point charges Q1 at'~> Q 2 at r2, .. , Qn at rn (ii) A line charge PL per unit length - l- JPL --dr 4rre 0 r L (iii) A surface charge Ps per unit area _l_J dS 41teo r Ps s (iv) A volume charge Pv per unit volume _1_ 47t€ 0 J vol Pv d(vol) r In each an assemblage of charges is considered and a summation of the potential contributions is made simple, for potential is a scalar quantity.

The potential Vat any point P(x, y) may be taken as V0 ln {(x +a) 2 + y 2 } volts. Find expressions for the electric field strength E, and volume charge density Pv at point P. y y P(x. y) 0(0. 9. 9b, a similar parallel line charged(+ PL) has been added through the point (+a, 0). Deduce an expression for the electric field strength Eo at any point Q(O, y) on they axis. If Eo must not exceed 500 kV/m, fmd the greatest permissible V0 for a = 1. 10 Three charges of values 47te 0 (+4, -3, +5) coulombs are established on con· ducting spheres each of 10 em diameter centred at points (30, 0, 0) (0, 40, 0) (0, 0, 50) em.

The components of curl Fare the circulations per unit area as the area tends to a point and are oriented perpendicular to the vectors ax, ay, Oz. The vector curl F is associated with closed paths in a vector field, and has no sources or sinks associated with it, in which case the divergence of curl F == 0. Curl F is thus solenoidal and an alternative criterion for a solenoidal field is that it must be expressible as the curl of a vector. 2 as an example of the use of Stokes's theorem. Note that 'V.

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