# Homework Help: Asking for hint to MTW's problem

1. Jan 11, 2012

### qinglong.1397

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

Page. 124, MTW Gravitation. Exercise 4.6.

Verify that the expressions given for the electromagnetic field of an oscillating dipole in equations (4.23) and (4.24) satisfy $dF=0$ everywhere and $d*F=0$ everywhere except at the origin.

2. Relevant equations

(4.23) $F=$real part of $\left\{p_1e^{iω(r-t)}[2\cos θ(1/r^3-iω/r^2)dr\wedge dt+\sin θ(1/r^3-iω/r^2-ω^2/r)rdθ\wedge dt+\sin θ(-iω/r^2-ω^2/r)dr \wedge rdθ]\right\}$

(4.24) $*F=$real part of $\left\{p_1e^{i(r-t)}[\sin \theta(-i\omega /r^2-\omega^2/r)dt \wedge r\sin\theta d\phi+2\cos\theta (1/r^3-i\omega /r^2)rd\theta \wedge r\sin\theta d\phi+\sin\theta (1/r^3-i\omega /r^2-\omega^2/r)r\sin\theta d\phi\wedge dr]\right\}$

3. The attempt at a solution

It is easy to show that $dF=0$ and $d*F=0$ everywhere except at the origin. But how to show $dF=0$ at the origin, while $d*F≠0$ at the origin?