CHAPTER 6 -- CLASSICAL ELECTROMAGNETISM
Electromagnetism describes the interaction of charged particles via electric and magnetic fields. It unifies electricity, magnetism, and optics.
6.1 ELECTRIC FIELDS
Electric Charge (q):
A fundamental property of matter. Charges can be positive or negative. Like charges repel; opposite charges attract. Charge is conserved.
Coulomb's Law:
The force between two point charges q1 and q2 separated by distance r is:
F = k_e * (q1 * q2) / r^2
where k_e is Coulomb's constant.
Electric Field (E):
Defined as the force per unit charge.
E = F / q
A point charge q produces a field:
E = k_e * q / r^2 * r_hat
Field lines point away from positive charges and towards negative charges.
6.2 MAGNETIC FIELDS
Magnetic fields (B) are produced by moving electric charges (currents) or intrinsic magnetic moments (spin).
- Permanent magnets have North and South poles. Field lines run from North to South outside the magnet.
- No magnetic monopoles have ever been observed (Gauss's Law for Magnetism).
6.3 LORENTZ FORCE
A charged particle q moving with velocity v in the presence of both an electric field E and a magnetic field B experiences the Lorentz Force:
F = q * (E + v x B)
- The electric force (qE) is parallel to the field.
- The magnetic force (q(v x B)) is perpendicular to both the velocity and the magnetic field.
- Magnetic forces do no work on charged particles because the force is always perpendicular to the displacement.
6.4 MAXWELL'S EQUATIONS
James Clerk Maxwell synthesized the laws of electricity and magnetism into four partial differential equations.
1. Gauss's Law for Electricity:
Div(E) = rho / epsilon_0
(Electric flux out of a volume is proportional to the enclosed charge).
2. Gauss's Law for Magnetism:
Div(B) = 0
(Magnetic flux out of a closed surface is zero; no magnetic monopoles).
3. Faraday's Law of Induction:
Curl(E) = - dB / dt
(A changing magnetic field induces a curling electric field).
4. Ampere-Maxwell Law:
Curl(B) = mu_0 * J + mu_0 * epsilon_0 * dE / dt
(Magnetic fields are generated by currents J and by changing electric fields).
6.5 EM WAVES
Maxwell's equations predict that oscillating electric and magnetic fields sustain each other and propagate through space as a wave.
- The wave equation derived from Maxwell's equations shows that these waves travel at a speed c = 1 / sqrt(mu_0 * epsilon_0).
- This value matched the measured speed of light, leading Maxwell to conclude that light is an electromagnetic wave.
- E and B are perpendicular to each other and to the direction of propagation (transverse waves).
6.6 RADIO WAVES
The electromagnetic spectrum ranges from radio waves (long wavelength, low frequency) to gamma rays (short wavelength, high frequency).
- Radio waves are generated by accelerating charges in antennas.
- They are used for communication (AM/FM radio, TV, Wi-Fi).
- Wavelengths range from millimeters to kilometers.
- Propagation behavior depends on frequency (e.g., skywave reflection by the ionosphere for shortwave radio).
