Prepare for Physics MSc exams
I have no special talents. I am only passionately curious.
- Plane polar form of position, velocity and accelaration
- Collision and linear momentum conservation
- Fictitious forces
- Centrifugal
- Coriolis force
- Azimuthal force
- Cools facts due to Coriolis force:
- Science behind tides
- Newton Gravitional problem(inverse square law,
$V(r) = -\frac{\alpha}{r^2}$ )(Klepler's problem )(Eccentricity$e = \sqrt{1+\frac{2EL^2}{m\alpha^2}}$ ) - Effective potential,
$V_{eff}(r) = \frac{L^2}{2mr^2} + V(r)$ - Three Conserved quatity
- Energy
- Angular momentum
- Runge-Lenz Vector(
$\vec A =$ constant vector)(for inverse square law$\vec A = \vec p \times \vec L - m \alpha \hat r$ )
- Cool problems in Central force field
- Captaring cross-section
- Scattering in a central force field
- Torque and angular momentum
- Moment of inertia
- Ellipsoid of inertia
$$I = I_{xx}\cos^2\alpha + I_{yy}\cos^2\beta + I_{zz}\cos^2\gamma + 2I_{xy}\cos\alpha\cos\beta + 2 I_{yz}\cos\beta\cos\gamma + 2I_{zx}\cos\gamma\cos\alpha$$ - Euler equation
- Kinematics
- Dynamics
- STR and eletro-magnetism
- Euler Lagrange equation
- From D'Alembert's principle
- From Stationary-action principle
- Legendre transformation
- Hamiltonian
- Advanced topics:
-
Noether's theorem:For each symmetry of the Lagrangian, there is a conserved quantity.
- Homogeneity of space
$\rightarrow$ conservation of linear momentum - Isotropy of space
$\rightarrow$ conservation of angular momentum - Time invarience
$\rightarrow$ conservation of energy
- Homogeneity of space
-
Noether's theorem:For each symmetry of the Lagrangian, there is a conserved quantity.
- Dirac Delta
Some cool problem can be dealt with Dirac delta function
- Coulomb's Law
- Electric Field
- Gauss's Law
- Electric Potential
- Electrostatic Boundary Conditions
- Work & Energy in Electrostatics
- Conductors
- Laplace's Equation
- Boundary Conditions & Uniqueness Theorem
- The Method of Images
- Multipole Expansion
- Dielectrics & Polarization
- Field of a Polarized Object
- Gauss's Law in Presence of Dielectrics
- Boundary Conditions
- Linear Dielectrics
- Energy in Dielectric Systems
- Forces on Dielectrics
- The Lorentz Force Law
- The Biot-Savart Law
- The Divergence and Curl of B
- Magnetic Vector Potential
- Magnetostatic Boundary Conditions
- Multipole Expansion of The Vector Potential
- Magnetization
- Torques and Forces on Magnetic Dipoles
- The Field of a Magnetized Object
- The Auxiliary Field H
- Ampere's law in Magnetized Materials * Boundary Conditions
- Linear and Nonlinear Media
- Magnetic Susceptibility and Permeability
- Ferromagnetism
- Electromotive Force
- Ohm's Law
- Electromotive Force
- Motional emf
- Electromagnetic Induction
- Faraday's Law
- The Induced Electric Field
- Inductance
- Energy in Magnetic Fields
- Maxwell's Equations
- Electrodynamics Before Maxwell
- How Maxwell Fixed Ampere's Law
- Maxwell's Equations
- Magnetic Charge
- Maxwell's Equations in Matter
- Boundary Conditions
- Solid state physics
- Diode
- Transistor
-
Sequential
- Clock
- Flipflop
- Register
-
Combinational
- Eigen value & Eigen vector
Huygen's principle: each point of a wavefront is a source of secondary disturbance and the wavelets emanating from these points spread out in all directions with the speed of the wave. The envelope of these wavelets gives the shape of the new wavefront.
- Interference
- Division of wavefront
- Young's double slit experiment
- Lloyd's mirror
- Fresnel biprism
- Fresnel two mirror
- Division of amplitude
- Thin flim interference
- Newton's ring
- Michelson's interferometer
- Multiple beam interferometer
- Febry-Perot interferometry
- Division of wavefront
- Diffraction
- Fraunhofer diffraction
- Fresnel diffraction
- Polarization
- The heart:
- Translational matrix
$$\begin{bmatrix}\lambda_2 \\ y_2 \end{bmatrix} = \begin{bmatrix}1 & 0 \\ \frac{L}{n} & 1 \end{bmatrix} \begin{bmatrix}\lambda_1 \\ y_1 \end{bmatrix}$$ - Refraction matrix
$$\begin{bmatrix}\lambda_2 \\ y_2 \end{bmatrix} = \begin{bmatrix}1 & \frac{n_1 - n_2}{R} \\ 0 & 1 \end{bmatrix} \begin{bmatrix}\lambda_1 \\ y_1 \end{bmatrix}$$ - Consequence from system of lens
- Unit planes and nodal plane
- Establish the lens maker formula
- Thin lens
- Equivalent focus of two thin lenses
- Oscilations
- Simple Pendulum
- Damped oscillator
- Forced oscillator
- Wave on a string
- Maxwell's distribution
- Einstein brownian motion
- Quantization of light
- Black-body radiation; Rayleigh-Jeans law
- Photoelectric effect
- Crompton effect
- Bohr model and atomic spectra
De Broglie's hypothesis brings the particle and wave theory into two sides of a same coin!
- Wave charecter of electron(i.e, matter wave)
- Davisson-Germer experiment
- Hisenberg uncertainty principle
- Boundary-value problems(1D problems)
- Infinite square well
- Step-potential
- Tunneling effect