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 ra, za, dE - 4T€,R² \ Vr dQ = P, dz R 3P Since for every dQ at z there is another charge dQ at -z, the z components cancel. Then Per dz 4TE(r² + z*)®z* E = Per. 4TE. Pe
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 ra, za, dE - 4T€,R² \ Vr dQ = P, dz R 3P Since for every dQ at z there is another charge dQ at -z, the z components cancel. Then Per dz 4TE(r² + z*)®z* E = Per. 4TE. Pe
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