E&M question.

  • Thread starter miew
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  • #1
miew
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Homework Statement



If the electric field in free space is E=Eo(x^+y^)sin(2pi/lamda)(z+ct), with Eo=2 statvolts/cm the magnetic field, not including any static magnetic field, must be what?

2. Relevant equation

∇ x B= 1/c ∂E/∂t

The Attempt at a Solution



First I calculated ∂E/∂t= cE0/c (x^+y^)cos(2pi/lamba)(x+ct)

Since B is perpendicular to E, it just has a z^ direction.

∇xB=∂yBzx^-∂xBzj^.

Then I equal both equations and I got Bz=Boc(yx^-xj^) cos....

Is this right ?
 

Answers and Replies

  • #2
betel
318
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I assume your hats mean unit vectors? So your E field is propagating in the z direction and the Field vector points in [tex]\hat x + \hat y[/tex]?

You made some mistake when you calculated [tex]\partial E/\partial t[/tex]. The argument inside the sine should not change and you get some additional factors.
You first guess for B is wrong. Z is not the only direction perpendicular to E.
 
  • #3
miew
27
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Yes, they are unit vector. And the x inside the sin it is supposed to be a z, sorry :/

So aren't there two directions in which B can be perpendicular? x+z and y+z ?
 
  • #4
betel
318
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There are two directions but in your first post you gave only one, z. And they are not the ones you gave in your last post.
In addition you only calculated [tex]B_z=..\hat x[/tex] as proportional to a vector. But Bz should just be a number.

Unless you know from somewhere else that E and B are perpendicular, so far from the equations you don't see it. In this case you would have to start with a general B.
 
  • #5
miew
27
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Okay, I start with a general B.

So then,
∂yBz-∂zBy= Eocos(A) (where A is everthing after cos)
∂zBx-∂xBz= Eocos(A)
∂xBy=∂yBx=0

Is that right ? if it is, how do I solve it ?
 
  • #6
betel
318
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Yes. The trick is to differentiate again and then combine the equations that you only have one B in the equation. Then you can integrate.
 
  • #7
miew
27
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Differentiate with respect to what ? :/
 
  • #8
betel
318
0
x,y,z. You just have to find the right combination.
 
  • #9
miew
27
0
Okay, I am going to try that !

Thanks :)
 

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