3 (a) ii) A time-dependent electric field in vacuum is given by(adsbygoogle = window.adsbygoogle || []).push({});

⃗E= E0(0, 0, sin(ky − ωt))

where E0 is a constant.

Derive an expression for the corresponding magnetic field ⃗B. [7]

Using curl E=-dB/dt

I end up with B=(E0/c)sin(ky-wt)

Show that both ⃗E and ⃗B are perpendicular to the wave vector ⃗k = (0, k, 0). [2]

Using the dot product i found that:

k.E=(0x0,0xk,0x ⃗E)=0

k.B=(0x ⃗E/c,0xk,0x0)=0

What is the Poynting vector for this wave? [4]

N=(ExB)/μ0μr

Then we get:

(1/μ0μr)((E0^{ 2}/c)sin(ky-wt)^{2},0,0)

Finally giving:

(-1/μ0.μr.c)(E0^{2}Sin(ky-wt)^{2})

I think the first two parts are right but have no idea if im doing the right thing on the last part. I have used the cross product between E and B and got my final answer for part 3. Thanks for any help in advance!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Electromagnetism, Poynting vector

**Physics Forums | Science Articles, Homework Help, Discussion**