Where Am I Going Wrong in Finding Radiation from an Oscillating Dipole?

[samjohnny]

Homework Statement

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.

 

[TSny]

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.

 

[samjohnny]

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?

 

[TSny]

Ah I believe that the derivatives must be evaluated at the retarded time, is that correct?

Yes.