Important Definitions & Formulas

Answer: Electric Charge: The intrinsic property of matter that causes it to experience a force in an electromagnetic field. SI Unit: Coulomb (C).

Quantization of Charge: The total charge on any object is always an integral multiple of the elementary charge ($e$). Formula: $q = \pm ne$, where $n = 1, 2, 3...$

Answer: Coulomb's Law: The electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.

Vector Form: $\vec{F}_{12} = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2} \hat{r}_{21}$

Answer: Dielectric Constant ($K$ or $\epsilon_r$): It is the ratio of the permittivity of the medium ($\epsilon$) to the permittivity of free space ($\epsilon_0$). Also defined as the ratio of electrostatic force between two charges in vacuum to the force between them in the medium. Formula: $K = \frac{\epsilon}{\epsilon_0} = \frac{F_{vacuum}}{F_{medium}}$.

Answer: Electric Field Intensity ($\vec{E}$): The electrostatic force experienced by a unit positive test charge placed at that point.
Formula: $\vec{E} = \lim_{q_0 \to 0} \frac{\vec{F}}{q_0}$.
SI Unit: N/C or V/m.

Answer: Electric Dipole: A system of two equal and opposite point charges separated by a small distance ($2a$).

Dipole Moment ($\vec{p}$): The product of the magnitude of either charge and the distance between them. Formula: $\vec{p} = q \times 2\vec{a}$. Directed from negative to positive charge. SI Unit: Coulomb-meter (C·m).

Answer: Electric Flux ($\Phi_E$): The total number of electric field lines passing normally through a given area. Formula: $\Phi_E = \oint \vec{E} \cdot d\vec{A}$. SI Unit: $N m^2/C$.

Gauss's Law: The total electric flux through any closed surface is equal to $1/\epsilon_0$ times the net charge enclosed by the surface. Formula: $\oint \vec{E} \cdot d\vec{A} = \frac{q_{enclosed}}{\epsilon_0}$.

Answer: Linear ($\lambda$): Charge per unit length. $\lambda = q/L$. Unit: $C/m$.

Surface ($\sigma$): Charge per unit area. $\sigma = q/A$. Unit: $C/m^2$.

Volume ($\rho$): Charge per unit volume. $\rho = q/V$. Unit: $C/m^3$.

Answer: Electric Potential ($V$): Work done by an external force in bringing a unit positive charge from infinity to a point without acceleration. $V = W/q_0$. SI Unit: Volt (V).

Potential Difference ($\Delta V$): Work done in moving a unit positive charge from one point to another in an electric field. $\Delta V = V_B - V_A = W_{AB}/q_0$.

Answer: Equipotential Surface: A surface over which the electric potential is constant at all points.

Properties: 1) No work is done in moving a charge on it. 2) Electric field is always perpendicular to it. 3) Two equipotential surfaces can never intersect.

Answer: The total work done by an external force in assembling a system of charges by bringing them from infinity to their present locations. Formula for two charges: $U = \frac{1}{4\pi\epsilon_0}\frac{q_1 q_2}{r}$.

Answer: Capacitance ($C$): The ratio of charge given to a conductor to the rise in its potential. $C = Q/V$. SI Unit: Farad (F).

Dielectric Polarization ($\vec{P}$): The induced dipole moment developed per unit volume of a dielectric when placed in an external electric field.

Answer: Energy Stored ($U$): The work done in charging a capacitor. $U = \frac{1}{2}CV^2 = \frac{Q^2}{2C} = \frac{1}{2}QV$.

Energy Density ($u$): Energy stored per unit volume of the electric field. $u = \frac{1}{2}\epsilon_0 E^2$.

Answer: Current Density ($\vec{J}$): Current flowing per unit area normal to the flow. $\vec{J} = I/A$.

Drift Velocity ($\vec{v}_d$): The average velocity with which free electrons get drifted towards the positive end of a conductor under an external electric field. $v_d = \frac{eE}{m}\tau$.

Relaxation Time ($\tau$): The average time interval between two successive collisions of free electrons.

Answer: Mobility ($\mu$): The magnitude of drift velocity per unit electric field. $\mu = v_d / E$.

Ohm's Law: At constant physical conditions, current is directly proportional to potential difference ($V=IR$).
Vector Form: $\vec{J} = \sigma \vec{E}$ (where $\sigma$ is conductivity).

Answer: Resistivity ($\rho$): Resistance of a conductor of unit length and unit area of cross-section. It depends only on material and temperature. $\rho = m / (ne^2\tau)$.

Internal Resistance ($r$): The resistance offered by the electrolyte and electrodes of a cell to the flow of current through it.

Answer: KCL (Junction Rule): Algebraic sum of currents meeting at a junction is zero (Conservation of Charge).
KVL (Loop Rule): Algebraic sum of changes in potential around any closed loop is zero (Conservation of Energy).

Wheatstone Bridge Balanced Condition: When galvanometer shows zero deflection, $P/Q = R/S$.

Answer: Lorentz Force: Total force on a charge $q$ moving with velocity $\vec{v}$ in combined $E$ and $B$ fields. $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$.

Biot-Savart Law: Magnetic field $dB$ due to a current element $Idl$ is proportional to current, length, sine of angle, and inversely to square of distance. $d\vec{B} = \frac{\mu_0}{4\pi} \frac{I(d\vec{l} \times \hat{r})}{r^2}$.

Answer: Ampere's Law: The line integral of magnetic field around any closed loop is equal to $\mu_0$ times the total steady current threading the loop. $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enclosed}$.

Magnetic Dipole Moment ($\vec{m}$): For a current loop, it is the product of current and area vector. $\vec{m} = NIA$. Unit: A·m².

Answer: Current Sensitivity: Deflection produced per unit current ($I_s = \theta/I = NAB/k$).
Voltage Sensitivity: Deflection per unit voltage ($V_s = \theta/V = NAB/kR$).

Conversion: To Ammeter: Connect a low resistance (shunt) in parallel. To Voltmeter: Connect a high resistance in series.

Answer: Magnetic Flux ($\Phi_B$): Total number of magnetic field lines passing normally through a surface. $\Phi_B = \vec{B} \cdot \vec{A}$. Unit: Weber (Wb).

Earth's Elements: 1) Declination (Angle between geographic and magnetic meridians). 2) Dip/Inclination (Angle Earth's net B-field makes with horizontal). 3) Horizontal Component ($B_H = B \cos\delta$).

Answer: Magnetization ($M$): Net magnetic moment developed per unit volume.
Susceptibility ($\chi$): Determines how easily a substance can be magnetized ($M = \chi H$).

Diamagnetic: Weakly repelled by magnets ($\chi$ is small and negative).
Paramagnetic: Weakly attracted ($\chi$ is small and positive).
Ferromagnetic: Strongly attracted ($\chi$ is very large and positive).

Answer: EMI: Phenomenon of inducing an EMF in a coil when the magnetic flux linked with it changes.

Faraday's Law: The magnitude of induced EMF is directly proportional to the rate of change of magnetic flux. $E = -\frac{d\Phi}{dt}$.

Lenz's Law: The direction of induced current is such that it opposes the very cause (change in flux) that produces it. (Consequence of Energy Conservation).

Answer: Self Induction ($L$): Property of a coil by which it opposes any change in its own current by inducing an EMF in itself. $E = -L(dI/dt)$.

Mutual Induction ($M$): Phenomenon of inducing an EMF in a secondary coil due to a change in current in a neighboring primary coil. $E_s = -M(dI_p/dt)$. Unit for both is Henry (H).

Answer: RMS Current: That steady current which produces the same heat in a resistor as the AC does in one full cycle. $I_{rms} = I_0 / \sqrt{2}$.

Reactance: Opposition offered by Inductor ($X_L = \omega L$) or Capacitor ($X_C = 1/\omega C$) alone.

Impedance ($Z$): Total effective opposition offered by an LCR circuit. $Z = \sqrt{R^2 + (X_L - X_C)^2}$.

Answer: Resonance: State when $X_L = X_C$, making impedance minimum ($Z=R$) and current maximum. Frequency $f_r = \frac{1}{2\pi\sqrt{LC}}$.

Power Factor: Ratio of true power to apparent power ($\cos\phi = R/Z$).

Wattless Current: The component of AC ($I_{rms} \sin\phi$) that does not consume any average power (occurs in purely inductive/capacitive circuits).

Answer: A device based on mutual induction used to increase or decrease alternating voltage.
Transformation Ratio ($k$): $k = N_s/N_p = V_s/V_p$. If $k > 1$, it is a step-up transformer.

Answer: Displacement Current: The equivalent current produced by a time-varying electric field in space (e.g., between capacitor plates). $I_d = \epsilon_0 \frac{d\Phi_E}{dt}$.

EM Waves: Transverse waves consisting of mutually perpendicular oscillating electric and magnetic fields. Velocity in vacuum: $c = 1/\sqrt{\mu_0\epsilon_0}$.

Answer: TIR (Total Internal Reflection): When light traveling from denser to rarer medium strikes the interface at an angle greater than the critical angle, it is completely reflected back.

Critical Angle ($C$): The angle of incidence in denser medium for which angle of refraction is 90°. $\sin C = 1/\mu$.

Answer: Lens Maker's: $\frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$. Power of lens $P = 1/f$ (in Diopters).

Magnifying Power ($M$): Ratio of angle subtended at eye by the image to the angle subtended by the object at the unaided eye. Telescope: $M = f_o/f_e$.

Answer: Angle of Minimum Deviation ($\delta_m$): The smallest angle of deviation produced by a prism when $i = e$. $\mu = \frac{\sin((A+\delta_m)/2)}{\sin(A/2)}$.

Resolving Power: Ability of an optical instrument to form distinct, separate images of two closely spaced objects.

Answer: Wavefront: The continuous locus of all particles vibrating in exactly the same phase.
Huygens' Principle: Every point on a wavefront acts as a fresh source of secondary wavelets.

Coherent Sources: Sources emitting light waves of same frequency and a constant phase difference.

Answer: Fringe Width ($\beta$): Distance between two consecutive bright or dark fringes. $\beta = \frac{\lambda D}{d}$.

Diffraction: Bending of light around sharp corners of an obstacle comparable to its wavelength.

Brewster's Law: At polarizing angle, reflected light is completely polarized. $\mu = \tan(i_p)$.

Answer: Work Function ($\Phi_0$): Minimum energy required to eject an electron from a metal surface.

Photoelectric Effect: Emission of electrons from metals when illuminated by light of suitable high frequency.

Stopping Potential ($V_0$): The minimum negative potential given to the anode to completely stop the fastest photoelectrons. $K_{max} = eV_0$.

Answer: Matter Waves: The wave associated with every moving material particle.
Formula: $\lambda = \frac{h}{p} = \frac{h}{mv} = \frac{h}{\sqrt{2mK}}$.

Answer: Impact Parameter ($b$): Perpendicular distance of the initial velocity vector of alpha particle from the central line of the nucleus.

Bohr's Quantization Postulate: Electrons revolve only in orbits where their angular momentum is an integral multiple of $h/2\pi$. ($L = mvr = nh/2\pi$).

Answer: Mass Defect ($\Delta m$): The difference between the sum of masses of individual nucleons and the actual mass of the nucleus.

Binding Energy: Energy required to break a nucleus into its constituent protons and neutrons completely. $BE = \Delta m \times c^2$.

Answer: Depletion Region: A thin layer around a p-n junction devoid of mobile charge carriers, containing only immobile ions.

Barrier Potential: The potential difference developed across the depletion layer opposing further diffusion of majority carriers.

Rectifier: A device using p-n junction diodes to convert AC (Alternating Current) into unidirectional DC (Direct Current).