How to put magnetic field in the wave equation

[fabsuk]

Could someone please help, i think this is gauss's law but I am not sure how to answer it as they give me a wave equation and i don't know how to put magnetic field in as well. Help would be much appreciated



Question


suppose that an appropriate device is used to genereate an osccilating electric field in a limited region of the xy plane of a Cartesian Reference frame ,as described by

E(r,t) ezE0sin(wt) for

√x(squared)+Y(squared) <(equal ) R

a) determine the expression for the magnetic field induced by this electric field in the xy plane at a distance r<R from the origin

b)at a distance r>R from the origin assuming that in the 1st approximation E=0 in this region

c) discuss if u would expect an induced an electric field to also be present in the region r>R of xy plane

 

[Physics Monkey]

Hi fabsuk,

You need to take a step back from the wave equation and look directly at the Maxwell equations. You know the electric field in some region and you want to find the magnetic field. This is will be possible because Maxwell's equations relate the two fields.

Try to make some progress with this hint, and let me know how you do.

 

[fabsuk]

yes but why do they give me an equation of a circlr

delta cross E= - db/dt

 

[fabsuk]

can't do it

i don't know what to differentiate E with respect to

i know the answer is 0 outside sphere but inside sphere i am clueless.

please help.

 

[Reshma]

can't do it

i don't know what to differentiate E with respect to

i know the answer is 0 outside sphere but inside sphere i am clueless.

please help.

Physics Monkey already gave you a clue . Use Maxwell's relation for the electric and magnetic vectors. OK here goes: If E and B represent the magnitude of the electric and magnetic fields respectively:
$${E\over B} = c = {{1\over \sqrt{\epsilon_o \mu_0}}$$