- #1
shevchenko12
- 3
- 0
3 (a) ii) A time-dependent electric field in vacuum is given by
⃗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)(E02Sin(ky-wt)2)
I think the first two parts are right but have no idea if I am 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!
⃗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)(E02Sin(ky-wt)2)
I think the first two parts are right but have no idea if I am 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!