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A proof of E for line charge distribution Charge is distributed uniformly along an infinite straight line with constant density Pe. Develop the expression for E at the general point P.

A proof of E for line charge distribution Charge is distributed uniformly along an infinite straight line with constant density Pe. Develop the expression for E at the general point P.

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A proof of E for line charge distribution Charge is distributed uniformly along an infinite straight line with constant density Pe. Develop the expression for E at the general point P. Cylindrical coordinates will be used, with the line charge as the z axis (see Fig. 2-14). At P, dQ dE = 4xE,R² \VF+z (ra,-za, too Pe IRI dQ = P. dz 3P - 00 Since for every dQ at z there is another charge dQ at -z, the z components cancel. Then Per dz E = Pe a, = 2nE,r Per
Transcribed Image Text:A proof of E for line charge distribution Charge is distributed uniformly along an infinite straight line with constant density Pe. Develop the expression for E at the general point P. Cylindrical coordinates will be used, with the line charge as the z axis (see Fig. 2-14). At P, dQ dE = 4xE,R² \VF+z (ra,-za, too Pe IRI dQ = P. dz 3P - 00 Since for every dQ at z there is another charge dQ at -z, the z components cancel. Then Per dz E = Pe a, = 2nE,r Per
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