Question

Using the Gauss's Law, find the expression of the electric field at a distance r from a line of positive charge of infinite length and constant linear charge density λ. 8.

Answer 1

The line of charge is infinitely long.Therefore,the field is the same at all points equidistant from the line ,regardless of the vertical position of the point .Because the charge is distributed uniformly along the line,the charge distribution has cylindrical symmetry and we can apply Gauss's law to find the electric field.

The line of charge is infinitely long. Therefore, the field is the same at all points equidistant from the line, regardless of the vertical position of the point .Because the charge is distributed uniformly along the line, the charge distribution has cylindrical symmetry and we can apply Gauss's law to find the electric field. Apply gauss law phi E = contourintegralE^bar.da^bar = E contourintegral dA = q_in/E_0 E contourintegral dA = -lambda l/E_0 E(2 pi r l) = lambda l/E_0 E = lambda l/(2 pi r l)E_0 = lambda/2 pi elementof_0 r E = 2 lambda/2(2 pi e_0 r) = 2 lambda/r) = 2 k_c lambda/r where k_c = coulombs constant = 8.99 times 10^9 N.m^2/c^2