Question

that depends points in the Fx direction but has a magnitude only on y has zero divergence E12B.3 Consider an electric field which everywhere points in the tz direction but has a magnitude that depends only on s, where E12B.4 Suppose that the electric field in a certain region of space is given by E - Jax, ay, ac] where a is a constant. What is the divergence El 2B,5 Suppose that the electric field in a certain region of space is axial (C-EA where, s a unit vector pointing directly away from the s vty is the distance from the z axis. What is the divergence of such a field? of this field in terms of a? axis) with E, -as where a is a constant. Calculate this field's divergence in terms of a

Answer 1

In this question, electric field is said to depend on S. S, (x^2 + y^2)^1/2 [not amen timed directly proportional or inversely proportional] In general Therefore E alpha y_s^2 Therefore E = k/s^2 Therefore = k/(x^2 + y^2) Because E vector = k/x^2 + y^2 z^^ In cartesian co-ordinate nabla^- E^- = Partialdifferential E_x/Partialdifferential x + Partialdifferential e_y/Partialdifferential y + Partialdifferential E_z/Partialdifferential z Here E_z = k/x^2 + y^2, E_x = 0, E_y = 0 Partialdifferential E_z/Partialdifferential z = 0 Therefore nabla vector E vector = 0 E vector = [ax, ay, az] E vector = ax i^^+ ay j^^+ az k^^ nabla vector E vector = Partialdifferential e_x/Partialdifferential x + Partialdifferential e_y/Partialdifferential y + Partialdifferential E_z/Partialdifferential z E_x = ax, E_y = ay, E_z = az Therefore nabla^- E^- = a + a + a = 3 a \r\n E vector = E_3 3^^ Therefore E vector = as s^^