- #1
jb646
- 12
- 0
This isn't really a homework problem, I just need to know how to do a problem similar to this one for the final and I don't want to fail, so I posted it here.
The problem is:
Given the electric field for a plane wave in free space: E(r,t)=E1cos(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]
The problem is:
Given the electric field for a plane wave in free space: E(r,t)=E1cos(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]