2024-04-11 Radiation Fields and potentials

Electromagnetic Radiation

• Transportation of electromagnetic energy through the Poynting vector

Forms of engineered electromagnetic radiation

• Electric dipole radiation
• Magnetic dipole radiation
• Arbitrary radiation

Radiation fields from dipoles start from retarded potentials

Characteristic Length Scales

• Size of oscillating dipole
• Wavelength of EM radiation
• Distance between field point and dipole

Example: 5g cell network

• $\lambda$ @28ghz is approx 1.1cm
• Antenna size ($\lambda /2$ to $\lambda /4$) d approx 0.25 to 0.55 cm
• Antenna range is approximately 10 miles

Wavelength is much much less then distance to field point

Question 11.1 and 11.2

11.1 Modify A

$$-\frac{{\mu }_0{p}_0\omega }{4\pi r}\left(\left[\sin \left(\omega \left(t-\frac{r}{c}\right)\right)\right]\cos \theta \hat{\mathbf{r}}-\left[\sin \left(\omega \left(t-\frac{r}{c}\right)\right)\right]\sin \theta \hat{\theta }\right)$$