# Radiation from Oscillating Dipole

1. Jan 18, 2016

### samjohnny

1. The problem statement, all variables and given/known data

2. Relevant equations

Given in the question.

3. The attempt at a solution

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.

2. Jan 18, 2016

### 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.

3. Jan 18, 2016

### samjohnny

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

4. Jan 18, 2016

Yes.