# 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

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.
P.S. Describing the physical nature of this wave? Do I need to state that the wave is linaear homogenous and Isotropic.