The problem is:

Given the electric field for a plane wave in free space: E(r,t)=E

_{1}cos(wt-ky)k

a)what is the statement for w and ka in the wave equation and how are they related to each other?

b)what is the direction of wave propagation?

c)write an expression for the accompanying magnetic field B

d)show that the electric field given above is is satisfied with the wave equation

relevant equations: since this is more of an explanation problem I worked the equations into the attempt at a solution

a)do I have to rearrange the equations to solve for w and k or do I just integrate to solve for them?

b)im pretty sure it is in the x-direction, that makes sense to me

c)∇xE=-(∂B/∂t)

so do I just calculate the cross products:

x y z

d/dx d/dy d/dz

E1cos(wt-ky) 0 E2cos(wt-ky)

and set that equal to -(∂B/∂t), if so, how to I un-partialize it [can you tell i'm not really a physics major, just taking a required class...sorry for the lack of terminology and general knowledge]