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## Question

Hi,

My textbook asks the question: The phase of an Electromagnetic wave at a point P at some instant is 5pi. Which of the following statements about the field vector is true?

A)Both the electric and the magnetic field vectors are 0

B)The electric field is 0 and the magnetic field has its maximum magnitude

C)The electric field has its maximum magnitude and the magnetic field is 0

D)Both the electric and magnetic field vectors have their max magnitudes.

My question for this question is, is the textbook talking about phase difference? If so, how can the magnetic field and the electric field have a phase difference since it is originating from the same source?

Thank you to all who take the time to reply to my question!

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Hi Lucy.  Without knowing the background (level) of the text and the context this is being asked in, it's a little difficult to explain exactly what you're looking for... In a plane electromagnetic wave, the plane of oscillation of the magnetic field and the electric field is offset by 90 degrees.  The wave travels in one direction, the electric field oscillates perpendicular to that direction, and the magnetic field oscillates perpendicular to both the wave velocity and the electric field oscillation.

http://www.aplusphysics.com/courses/honors/optics/EMSpectrum.html

Note that for a plane wave the electric field and magnetic field oscillations are in phase (at the same point in time they're both maximum or minimum).  Therefore, you could eliminate answers B and C.  Then, depending on whether you're representing your waves as sines or cosines, the correct answer could be A or D.

To choose between A or D, look at the function you're using to model the waves and its value at time t=0.  With a phase change of 5Pi, you'll have the opposite situation you would have at time t=0.  So for a basic cosine function modeled so that the E field has a maximum value at time t=0, at the instant in time where the phase is 5Pi, it would be at a minimum (0) value, so the answer would be A.  If you are modeling the wave so that the minimum value is exhibited at time t=0, you would have a maximum magnitude at phase 5Pi.

Hope this helps!

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Hi Mr. Fullerton,

Thank you so much for your swift response. However, I am not sure I understand what you mean in:

To choose between A or D, look at the function you're using to model the waves and its value at time t=0.  With a phase change of 5Pi, you'll have the opposite situation you would have at time t=0.  So for a basic cosine function modeled so that the E field has a maximum value at time t=0, at the instant in time where the phase is 5Pi, it would be at a minimum (0) value, so the answer would be A.  If you are modeling the wave so that the minimum value is exhibited at time t=0, you would have a maximum magnitude at phase 5Pi.

How do you know that the model of a Electromagnetic wave is cosine? Also, how do you know that the mininum vector is at 0(I know this is the only option but is there a way you would know this if the minimum was not given to you)?

Thank you so much for taking the time to answer my question!

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Typically books model EM wave functions with cosines, but I'd check your particular book that this question came from.  You know the minimum magnitude must be zero for an EM wave, as it follows a sine/cosine curve (max amplitude, 0, min amplitude, 0, max amplitude), etc.  I'm probably not helping a whole lot, but for further details, you may have to go dig back in the specific book you're looking at for the conventions they're using.

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