Problem with a Travelling Electromagnetic Wave

[Dante Tufano]

13.
A plane electromagnetic wave is traveling in the negative y direction. At t=0, the magnetic field at the origin has its maximum magnitude of 5.300×10-7 T and points in the positive x direction. Which axis does the electric field lie along? Answer with a single letter: x, y, or z. WARNING: You have only one try for this problem.

14.
The plane EM wave above also has a wavelength of 680 nm. Enter the formula for the component of the electric field along the axis from the previous question. Enter the formula as you might on a fancy calculator, for example

5.0 + 3.0*x^4 -0.110*sin(68.0*t)

Your formula should only have numbers and whichever of the variables x, y, z, or t are appropriate. The formula must be accurate for any position and any time. Put all numbers into SI units, but do not include units in the formula that you enter.

Okay, so I'm only having trouble with number fourteen, since it's fairly obvious that the electromagnetic field will point in the direction of the z-axis. I know that for an EM wave traveling in the positive x-direction that:

E=E_msin(kx-wt)

Thus, I've assumed that since the EM wave is traveling in the negative y-direction, that:

E=E_msin(-ky-wt)

So I've plugged and chugged, using:
c=(wavelength)*f
c=(angular freq.)/k
E_m/B_m=c

And I got 159.0*sin(-9.23997e6*y-2.77199e15*t) as the equation, but this is apparently wrong. Any ideas on where I may have messed up? (I know that there are many possible places)

 

[_coyote_]

It looks like you made a mistake in the formula. The equation should be E=Emsin(ky-wt). Since the wave is traveling in the negative y direction, the ky term should have a negative sign, not the -ky term. So the correct equation should be E=Emsin(-ky-wt).