By J.E. Parton
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Additional resources for Applied Electromagnetics
If there are n dipoles in a volume I m 3 of dielectric then P = total dipole moment per unit volume = np = nQd. Thus for a general volume (vol) in which there are N dipoles and n = N/(vol) polarisation P = (Q1 d 1 + Q2d2 + ... + QNdN )/(vol) = (PI + P2 + ... + Pm + ... + PN )/(vol) This is a vector summation. By and large, the polarisation has been produced by the action of the electric field and we can assume proportionality and write N P= L Pm/(vol)=Xe€oE m=l In this Xe is the proportionality constant, called electric susceptibility (chie).
4 which is of a finite line extending 0 to A on the z axis, charged with PL coulombs/m. It is customary to refer to distributed charge with the symbol P and a suffix L, S and V to indicate line, surface and volume charge respectively. This must not be confused with P z I I I I Bt"----- a dE, -----~----I.. P dE. 4 Field due to a line charge PL coulombs per metre. THE ELECTRIC FIELD 25 used as a coordinate in the cylindrical polar system or with the same symbol commonly used for resistivity. We wish to ftnd the electric fteld strength E at P due to this charged line.
An infinite uniform line charge PL = 2 nC/m lies on a line defined by = 3az , where r =xax + yay + zaz from the origin to a point on the line. Find the electric field strength E at (0, 5, 0) and at (1, 2, 6). 3 An infinite sheet with surface charge Ps = 12€o C/m2 is lying in the plane x - 2y + 3z = 4. Find an expression for the electric field strength E on the side of the plane including the origin. 4 (a) A line charge of 1 nC/m in a ring of 0·5 m radius is centred at (0, 0, 0) in the z = 0 plane.
Applied Electromagnetics by J.E. Parton