# Magnetic field from electric field given a function of time

## Homework Statement

An em wave in free space has an electric field vector E = f(t-z/c0)x where x is a unit vector in the x direction and f(t)= exp(-t22)exp(j2πv0t). Describe the physical nature of this wave and determine an expression of the magnetic field vector.

## Homework Equations

Maxwells faradays law ∇XE=-μ δH/δt

3. The Attempt at a Solution [/B]
I have two things I´m not so sure about. Given f(t) will the electric field now become
E= exp(-(t-z/c0)22)exp(j2πv0(t-z/c0))x

If so, when I use the curl of the field (dEz/dy-dEy/dz)x+(dEx/dz-dEz/dx)y+(dEy/dx-dEx/dy)z
I assume everything is 0 except for dEx/dz which I´m not sure because it´s multiplied by a unit vector y.
when I derivate by z I then have to intergrate by on both sides of the max eq. but I get a very complex integral.
So where I did I get lost.
Thanks in advance.
P.S. Describing the physical nature of this wave? Do I need to state that the wave is linaear homogenous and Isotropic.

## Answers and Replies

Hi. For the physical nature of the wave, you can ask yourself: is it polarized, and if yes in which direction? is it propagating, and if it is in which direction? how is the amplitude: constant or changing?
For the B field, you can start by determining the charges and currents present. Then you should be able to use Maxwell's equations to determine a simpler relation between E and B...

Scratch the second part of my answer, you can actually use ∇ × E = –μ ∂B/∂t directly, as you started:
the curl is easy to take, then integrating with respect to time becomes easy as well since t and z/c0 enter in the equation in (anti-)symmetric way...