Question

Please help me, i'll give u medal.. a sinusoidal electromagnetic wave with a frequency of 1.5x 10 ^ 15 Hz propagates in vacuum in the positive y-axis direction. Magnetic field is parallel to the x axis with an amplitude of 3 mT. When y = 0 and t = 0, the large magnetic field is 0. Determine the function of the wave vector of the magnetic field and electric field at the time t.

Answer 1

Use this,

\[\huge B(r,t)=B_0 e^{-(k.r - wt)}\]
\[\huge E(r,t)=E_0 e^{-(k.r - wt) }\]

E_0 and B_0 are amplitudes,k is the wave vector and w is the cycle frequency

Also
\[r = x i + y j + z k \]
r is vector

Also .
\[c =(\lambda )(frequency)\]
Therefore
\[\lambda = {{c } \over {frequency}}\]
c-->speed of light

Also
k is the wave vector
\[k = {{2(pi)}\over{\lambda}}\]

Now try to do the problem :)

Answer 2

also to add up x = ct

Answer 3

and \( \omega = 2 \pi f\)

Answer 4

i can't get the r.. what is r?

Answer 5

r is a vector. I have also defined r above. In the question,
For magnetic field,
r = x i
(because magnetic field is acting along x-axis)

Answer 6

\[B _{0}e ^{-(2[pi]ft\ i - 2[pi]ft)}\]

Answer 7

like that?

Answer 8

Yes @iasazhary . Now, in the question, B_0 is given , f is given . That's all
Now find E vector

Answer 9

\[so\ B(r,t)=B_{o}e^{0}\ ?\]

Answer 10

for simplicity's sake just put

\( B = B_0 \sin(kx+\omega t)\)

Answer 11

oh, x=/=ct okay i get it.. thank you @shivam_bhalla and @experimentX ..

Answer 12

x=/ ??

Answer 13

and don't forget the standard equation above ..

Answer 14

@experimentX , just a question to you. The equation I mentioned and the equation you mentioned are 2 different forms of the same equation or they are 2 different equations?

Answer 15

no .. the equation you wrote is standard electromagnetic equation in 3d space ... the one i wrote is plane progressive equation in 1-d

Answer 16

@shivam_bhalla because x is variable. so it can't be subtituted with ct .. so x isn't ct..

Answer 17

@experimentX okay, that standard electromagnetic is greatly simplify the equation..

Answer 18

Oh @iasazhary , I didn't understand what "=/=" meant . That's why I got confused :)

Answer 19

@experimentX , Thanks for explaining :D

Answer 20

not really, i haven't understood these things pretty much.
@iasazhary well, since we have having progressive wave in 1-d ... it is better to use my equation instead of shivam_bhalla's ... and also these fields are vectors R is a vector, and these complex number's seem to deal with wave's more easily than with usual trigonometric function i guess that what shivam_bhalla wrote must be the standard one.