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Radiation from Oscillating Dipole

  • Thread starter samjohnny
  • Start date
  • #1
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Homework Statement



Dipole.png


2. Homework Equations [/B]

Given in the question.

The Attempt at a Solution


[/B]
For part a I obtained an expression for the the dipole moment:

##P(t)= P_0 cos(wt)##

And therefore, for part b, I obtained the expressions

##\frac{dP}{dt} = -wP_0 sin(wt)## and ##\frac{d^2P}{dt^2} = -w^2P_0 cos(wt)##.

Now when I make use of Eq. 1.39 to obtain ##E_\theta## for part c), I substitute in the above expression for ##\frac{d^2P}{dt^2}##, but end up with the cos term being ##cos(wt)## from ##\frac{d^2P}{dt^2}## as opposed to ##cos(kr-wt)## which is required. Not sure where I'm going wrong.
 

Answers and Replies

  • #2
TSny
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In Eq. 1.39, the square brackets in the numerators denote a condition on the time at which you evaluate the quantities inside the brackets. Check your notes or text for details.
 
  • #3
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In Eq. 1.39, the square brackets in the numerators denote a condition on the time at which you evaluate the quantities inside the brackets. Check your notes or text for details.
Ah I believe that the derivatives must be evaluated at the retarded time, is that correct?
 
  • #4
TSny
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Ah I believe that the derivatives must be evaluated at the retarded time, is that correct?
Yes.
 

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