Notes from Toppers
Magnetic Fields and EM Waves
Magnetic Fields
- Biot-Savart Law:
- Mathematical expression: $$d \vec{B}={\mu_0}{id\vec{l}\times\hat{r}}\over{4\pi r^2}$$
- Ampère’s Law:
- Relationship between magnetic field and current: $$\sum \vec{B}\cdot d\vec{l}=\mu_0 I_{enc}$$
- Applications in finding the magnetic field created by simple current-carrying conductors like straight wires, solenoids, and toroids.
Electromagnetic Induction
- Faraday’s Law:
- Induced EMF: $$\mathcal{E}=-\frac{d\Phi_B}{dt}$$
- Lenz’s Law:
- Determining the direction of induced EMF and current.
- Applications: Generators, transformers, and motors.
- Motional EMF: $$\mathcal{E}=vBL\sin\theta$$
EM Waves
- Maxwell’s Equations:
- Four fundamental equations governing electromagnetic phenomena.
- Wave Equation:
- Describes the propagation of electromagnetic waves: $$\left( \frac{\partial^2}{\partial t^2}-v^2\nabla^2\right) \vec{E}=0$$
- Transverse Nature:
- Oscillations are perpendicular to the direction of propagation.
- Plane EM Waves:
- Mathematical description: $$\vec{E}=\hat{E_0} \cos(kz-\omega t)$$
- Energy Density and Power:
- Poynting vector: $\vec{S}=\frac{1}{\mu_0}\vec{E}\times\vec{B}$
Additional Concepts:
- Displacement Current:
- Maxwell’s addition to Ampere’s law: $$I_d=\epsilon_0\frac{d\Phi_E}{dt}$$
- Boundary Conditions:
- Relations for EM fields at interfaces between different media.
- Reflection and Refraction:
- Behavior of EM waves at dielectric interfaces.
- Polarization:
- Linear, circular, and elliptical polarization states.
References
- NCERT Physics, Class 11: Chapter 4 (Motion in a Plane), Chapter 5 (Laws of Motion), Chapter 6 (Work, Energy, and Power).
- NCERT Physics, Class 12: Chapter 6 (Electrostatics), Chapter 7 (Current Electricity), Chapter 8 (Magnetic Effects of Current), Chapter 9 (Electromagnetic Induction).