Question

Problem 3 in the diagram below, Infinite rod carry a charge density of -cX с 10-6 C int P if the the distance from the center of the rod to point P is a 0.8 m Please show all the steps needed to get the final equation of the E field then find the magnitude and direction of the E at point P Take five points a long the doted line and calculate the magnitude and direction of the E field along the line.

Answer 1

When we had a finite line of charge we integrated to find the field. We could do that again, integrating from minus infinity to plus infinity, but it is a lot easier to apply Gauss law. First, let's agree that if the charge on the line is positive the field is directed radically out from the line. If negative the field is directed in Assume Gaussian surface Total charge enclosed is q_ene = lambda L Net flux = EA = E(2 pi a)L By hours law the net flux = q_ene/epsilon therefore E/2 pi a /l = lambda L/epsilon_0 E = lambda /2 pi epsilon_0 alpha E = 2 lambda/4 pi epsilon_0 alpha = 2 k lambda/alpha E = 2 times 9 times 10^9 times (-c x)/0.8