JEE Physics Electricity Optics and Modern Physics Notes Set 01

Electrostatics and Current Electricity

1. Gauss's law: flux through a closed surface is \(q_{in}/\epsilon_0\). A charge at the centre of a cube sends one sixth of its flux through each face. Build a bigger cube using symmetry when the charge is off-centre.
2. Electrostatic pressure on a conductor surface: \(\dfrac{\sigma^2}{2\epsilon_0} = \dfrac{\epsilon_0E^2}{2}\), directed outward.
3. Capacitors: parallel \(C = C_1 + C_2\), series \(\dfrac1C = \dfrac1{C_1} + \dfrac1{C_2}\). Charge drawn from the cell is \(C_{eq}V\).
4. Potentiometer: internal resistance \(r = R\left(\dfrac{l_1}{l_2} - 1\right)\) when the cell is shunted by R.
5. Bulb resistance is fixed by its rating: \(R = V^2/P\).

Magnetism, Induction and AC

1. Right-hand grip rule gives the direction of the field of a long straight wire. Fields of antiparallel currents add between the wires.
2. Charge through a coil: \(q = \Delta\Phi/R\), equal to the area under the \(i\)-\(t\) graph.
3. For \(I = I_0\sin(\omega t + \phi)\), the current is first maximum when \(\omega t + \phi = \pi/2\).
4. Electromagnetic waves are transverse, produced by accelerated charges and travel at c in vacuum only.

Optics

1. Plane mirror turned through \(\theta\) rotates the reflected ray through \(2\theta\).
2. Magnification graph: \(|1/m| = u/f - 1\), slope \(1/f\), intercept on the u axis \(= f\).
3. Fringe width \(\beta = \lambda D/d\). A thin sheet of thickness t and index \(\mu\) shifts the fringes by \((\mu - 1)tD/d\), where d is the slit separation.

Modern Physics and Electronics

1. Photon energy and wavelength: \(\lambda\,(\text{nm}) = 1240/E\,(\text{eV})\).
2. Radioactive decay: remaining fraction \((1/2)^{n}\) after n half-lives.
3. Binding energy per nucleon peaks near A = 56.
4. Diodes: a reverse-biased diode is open. A zener diode carries its maximum current when the load draws none.
5. Avalanche breakdown occurs by impact ionisation of minority carriers in a wide depletion layer.