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CLASS 12 • PHYSICS
Electromagnetic Waves
1. Displacement Current
Displacement Current ($I_d$)
$I_d = \epsilon_0 \frac{d\Phi_E}{dt}$
Due to changing Electric Flux
Ampere-Maxwell Law
$\oint \vec{B} \cdot d\vec{l} = \mu_0 (I_c + I_d)$
$I_c$ is Conduction Current
Inside Capacitor
$I_c = I_d$
Current is continuous
2. Wave Properties
Speed of Light
$c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} = 3 \times 10^8$
Relation E and B
$c = \frac{E_0}{B_0} = \frac{E_{rms}}{B_{rms}}$
E is much larger than B
Velocity in Medium
$v = \frac{1}{\sqrt{\mu \epsilon}} = \frac{c}{n}$
3. Energy & Momentum
Energy Density ($u_{avg}$)
$u = \frac{1}{2}\epsilon_0 E^2 + \frac{B^2}{2\mu_0}$
Electric & Magnetic parts are EQUAL
Intensity (I)
$I = u_{avg} \times c$
Power per unit Area
Momentum (p)
$p = \frac{U}{c}$
U = Total Energy
4. The Spectrum (Source & Use)
| Wave | Freq (Hz) | Source | Use |
|---|---|---|---|
| Radio | $10^4-10^9$ | Rapid acceleration of electrons in wires | Communication (TV, Radio) |
| Micro | $10^9-10^{11}$ | Klystron or Magnetron Valve | Radar, Microwave Ovens |
| Infra | $10^{11}-10^{14}$ | Vibration of atoms/molecules | Remotes, Physio, Haze Photo |
| Visible | $10^{14}$ | Electrons in atoms | Vision, Photography |
| UV | $10^{15}-10^{17}$ | Inner shell electrons, Sun | Water Purification, LASIK |
| X-Rays | $10^{17}-10^{19}$ | Bombarding metal with electrons | Medical Imaging, Bone scan |
| Gamma | $>10^{19}$ | Radioactive decay of nucleus | Cancer Treatment |
5. Common Exam Traps
- ⚠️ Direction of Wave: The wave travels in the direction of $\vec{E} \times \vec{B}$. It is perpendicular to BOTH E and B.
- ⚠️ Phase Difference: Electric field and Magnetic field oscillate in the SAME PHASE. (Zero phase difference).
- ⚠️ Energy Ratio: Energy is shared equally ($1:1$) between Electric and Magnetic fields.
6. Golden Theory Rules
- Source: Accelerated charges radiate electromagnetic waves.
- Oscillating Charge: Frequency of EM wave = Frequency of oscillation of charge ($f = 1/2\pi\sqrt{LC}$).
- Radiation Pressure: EM waves carry momentum, so they exert pressure on surfaces they hit.
