Electric Charges and Fields

• Physics is the study of the basic laws of nature and their manifestation in different phenomena.

Electric Charges and Fields

• Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field.
• There are two types of electric charges: positive and negative.
• Like charges repel each other, and unlike charges attract each other.
• Charge is quantized, existing in discrete packets that are integer multiples of the elementary charge (e ≈ 1.602 × 10-19 C).
• Charge is conserved; the total charge in an isolated system remains constant.
• Coulomb's Law: The electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
• Superposition Principle: The total force on a charge due to multiple charges is the vector sum of the forces due to each individual charge.
• Electric field is the region surrounding an electric charge in which another charge experiences a force.
• Electric field lines are a way to visually represent electric fields, showing the direction of the force on a positive test charge.
• Electric dipole is a pair of equal and opposite charges separated by a small distance.
• The dipole moment (p) measures the strength of an electric dipole and is defined as the product of the magnitude of either charge and the separation distance.
• Torque on a dipole in a uniform electric field: τ = pE sinθ, where θ is the angle between the dipole moment and the electric field.
• Electric flux measures the number of electric field lines passing through a given area.
• Gauss's Law: The total electric flux through a closed surface is proportional to the enclosed electric charge.
• Applications of Gauss's Law include finding the electric field due to uniformly charged objects like spheres, cylinders, and infinite sheets.

Electrostatic Potential and Capacitance

• Electric potential is the work done per unit charge to move a test charge from a reference point to a specific point in an electric field.
• Potential difference is the difference in electric potential between two points.
• Electric potential due to a point charge: V = kQ/r, where k is Coulomb's constant, Q is the charge, and r is the distance from the charge.
• Electric potential due to a dipole depends on the distance from the dipole and the angle relative to the dipole axis.
• Equipotential surfaces are surfaces with a constant electric potential.
• Electric field is always perpendicular to equipotential surfaces.
• Capacitance is the ability of a conductor to store electric charge.
• A capacitor is a device designed to store electrical energy by accumulating electric charge between two conductors (plates) separated by an insulator (dielectric).
• Capacitance (C) is defined as the ratio of charge (Q) stored on a conductor to the potential difference (V) between the conductors: C = Q/V.
• Parallel plate capacitor: C = ε0A/d, where ε0 is the permittivity of free space, A is the area of the plates, and d is the separation between the plates.
• Dielectric constant (κ) is the factor by which the capacitance increases when a dielectric material is inserted between the plates of a capacitor.
• Energy stored in a capacitor: U = (1/2)CV^2 = (1/2)QV = (1/2)(Q^2)/C.
• Capacitors in series: 1/Ceq = 1/C1 + 1/C2 + ...
• Capacitors in parallel: Ceq = C1 + C2 + ...

Current Electricity

• Electric current is the rate of flow of electric charge through a conductor.
• Current (I) is defined as the amount of charge (Q) flowing through a cross-sectional area per unit time (t): I = Q/t.
• Drift velocity is the average velocity of charged particles in a conductor due to an electric field.
• Ohm's Law: The potential difference (V) across a conductor is directly proportional to the current (I) flowing through it: V = IR, where R is the resistance.
• Resistance (R) is the opposition to the flow of electric current.
• Resistivity (ρ) is a material property that measures its resistance to electric current.
• Conductivity (σ) is the reciprocal of resistivity (σ = 1/ρ).
• Temperature dependence of resistance: Resistance of most conductors increases with temperature.
• Electrical energy is the energy transferred due to the flow of electric current.
• Electrical power is the rate at which electrical energy is consumed or dissipated.
• Power (P) is given by P = VI = I^2R = V^2/R.
• Cells, EMF, Internal Resistance: An electrochemical cell maintains a potential difference across its terminals by converting chemical energy into electrical energy.
• Electromotive force (EMF) is the potential difference across the terminals of a cell when no current is flowing.
• Internal resistance (r) is the resistance within the cell itself.
• Series and parallel combinations of resistors: Resistors in series add directly (Req = R1 + R2 + ...), while resistors in parallel combine reciprocally (1/Req = 1/R1 + 1/R2 + ...).
• Kirchhoff's laws:
• Kirchhoff's Current Law (KCL): The sum of currents entering a junction is equal to the sum of currents leaving the junction.
• Kirchhoff's Voltage Law (KVL): The sum of the potential differences around any closed loop in a circuit is zero.
• Wheatstone bridge is a circuit used to measure an unknown resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown resistance.
• Potentiometer is a device used to measure potential difference accurately without drawing current from the circuit.

Moving Charges and Magnetism

• Magnetic force: A moving charge experiences a force in a magnetic field.
• Magnetic force on a moving charge: F = q(v x B), where q is the charge, v is the velocity, and B is the magnetic field.
• Lorentz force is the total force on a charged particle due to both electric and magnetic fields.
• Motion of a charged particle in a magnetic field:
• If the velocity is perpendicular to the magnetic field, the particle moves in a circular path.
• If the velocity has a component parallel to the magnetic field, the particle moves in a helical path.
• Cyclotron is a particle accelerator that uses a magnetic field to bend charged particles into a spiral path, increasing their energy.
• Magnetic force on a current-carrying conductor: F = I(L x B), where I is the current, L is the length of the conductor, and B is the magnetic field.
• Force between two parallel current-carrying conductors: Parallel currents attract, and antiparallel currents repel.
• Ampere's Law relates the integrated magnetic field around a closed loop to the current passing through the loop.
• Magnetic field due to a straight wire: B = (μ0I)/(2πr), where μ0 is the permeability of free space, I is the current, and r is the distance from the wire.
• Magnetic field due to a circular loop: at the center, B = (μ0I)/(2R), where R is the radius of the loop.
• Magnetic dipole: a small current loop behaves as a magnetic dipole.
• Magnetic dipole moment (m) is the product of current and the area of the loop.
• Torque on a magnetic dipole in a uniform magnetic field: τ = mB sinθ, where θ is the angle between the dipole moment and the magnetic field.
• Moving Coil Galvanometer: A galvanometer is a device used to detect and measure small electric currents.

Magnetism and Matter

• Magnetism arises from the intrinsic magnetic moments of electrons.
• Magnetic materials are classified as diamagnetic, paramagnetic, or ferromagnetic based on their response to an external magnetic field.
• Diamagnetic materials are weakly repelled by a magnetic field.
• Paramagnetic materials are weakly attracted by a magnetic field.
• Ferromagnetic materials are strongly attracted by a magnetic field and can be permanently magnetized.
• Magnetic susceptibility (χ) measures how easily a material can be magnetized.
• Permeability (μ) measures how much a material concentrates magnetic field lines.
• Hysteresis is the lagging of magnetization behind the magnetizing field in a ferromagnetic material.
• Earth's magnetism: The Earth behaves as a giant magnet.
• Magnetic declination is the angle between the geographic north and the magnetic north.
• Magnetic dip is the angle between the Earth's magnetic field and the horizontal.

Electromagnetic Induction

• Electromagnetic induction is the phenomenon of inducing an electromotive force (EMF) in a conductor by changing the magnetic field around it.
• Faraday's Law of Induction: The induced EMF in a closed loop is equal to the negative of the rate of change of magnetic flux through the loop.
• Lenz's Law: The direction of the induced current is such that it opposes the change in magnetic flux that produces it.
• Motional EMF is the EMF induced in a conductor moving through a magnetic field.
• Induced electric fields are produced by changing magnetic fields, even in the absence of a conductor.
• Self-inductance is the property of a coil to oppose changes in current flowing through it.
• Inductance (L) measures self-inductance.
• Energy stored in an inductor: U = (1/2)LI^2.
• Mutual inductance is the phenomenon where a changing current in one coil induces an EMF in a nearby coil.
• AC generator: A device that converts mechanical energy into electrical energy in the form of alternating current.

Alternating Current

• Alternating current (AC) is an electric current that periodically reverses direction and changes its magnitude continuously with time.
• AC voltage is a voltage that varies sinusoidally with time.
• Root mean square (RMS) value of AC: The effective value of AC voltage or current is the RMS value.
• Reactance opposes the flow of AC by inductors and capacitors.
• Inductive reactance (XL) is proportional to the frequency of the AC and the inductance.
• Capacitive reactance (XC) is inversely proportional to the frequency of the AC and the capacitance.
• Impedance (Z) is the total opposition to the flow of AC in a circuit, combining resistance and reactance.
• Series LCR circuit: A circuit containing an inductor, a capacitor, and a resistor connected in series.
• Resonance is a condition in an LCR circuit when the inductive reactance equals the capacitive reactance, resulting in maximum current flow.
• Power in AC circuit: Average power dissipated in an AC circuit depends on the voltage, current, and phase angle between them.
• Power factor is the cosine of the phase angle between voltage and current.
• Transformer is a device that changes the voltage of an AC supply using the principle of mutual induction.

Electromagnetic Waves

• Electromagnetic waves are transverse waves consisting of oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation.
• Electromagnetic spectrum includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays, differing in frequency and wavelength.
• Properties of electromagnetic waves: They travel at the speed of light in vacuum, carry energy and momentum, and can exhibit interference and diffraction.

Ray Optics and Optical Instruments

• Reflection is the bouncing back of light when it strikes a surface.
• Laws of reflection: The angle of incidence equals the angle of reflection, and the incident ray, reflected ray, and normal lie in the same plane.
• Refraction is the bending of light as it passes from one medium to another.
• Laws of refraction: Snell's law (n1sinθ1 = n2sinθ2), and the incident ray, refracted ray, and normal lie in the same plane.
• Total internal reflection occurs when light traveling from a denser medium to a rarer medium strikes the interface at an angle greater than the critical angle.
• Optical fiber works on the principle of total internal reflection.
• Lenses are curved pieces of transparent material that refract light to form images.
• Lens maker's formula relates the focal length of a lens to its refractive index and the radii of curvature of its surfaces.
• Thin lens formula relates the object distance, image distance, and focal length of a thin lens.
• Magnification is the ratio of the size of the image to the size of the object.
• Optical instruments:
• Microscope: An instrument used to magnify small objects.
• Telescope: An instrument used to view distant objects.

Wave Optics

• Wave optics deals with the phenomena of interference, diffraction, and polarization, which demonstrate the wave nature of light.
• Huygens' principle: Every point on a wavefront is a source of secondary wavelets that spread out in all directions with the same speed as the wave.
• Interference is the superposition of two or more waves, resulting in constructive or destructive interference.
• Young's double-slit experiment demonstrates the interference of light waves, creating an interference pattern of bright and dark fringes.
• Diffraction is the bending of waves around obstacles or through apertures.
• Single-slit diffraction: A single slit produces a diffraction pattern with a central bright maximum and alternating dark and bright fringes.
• Polarization is the phenomenon where the vibrations of light waves are restricted to a single plane.
• Polarizing filters are used to produce polarized light.

Dual Nature of Radiation and Matter

• Photoelectric effect is the emission of electrons from a metal surface when light shines on it.
• Einstein's photoelectric equation relates the energy of the incident photon to the kinetic energy of the emitted electron and the work function of the metal.
• Matter waves: de Broglie proposed that matter exhibits wave-like properties.
• de Broglie wavelength is inversely proportional to the momentum of the particle.

Atoms

• Atomic models: Thomson's model, Rutherford's model, and Bohr's model.
• Bohr's postulates: Electrons revolve around the nucleus in specific orbits without emitting radiation, and electrons can only transition between orbits with specific energy levels.
• Energy levels of hydrogen atom: The energy levels are quantized and inversely proportional to the square of the principal quantum number.
• Atomic spectra: Emission and absorption spectra provide information about the energy levels in atoms.

Nuclei

• Nuclear structure: Nucleus consists of protons and neutrons.
• Nuclear size is very small compared to the size of the atom.
• Nuclear forces are strong, short-range forces that hold the nucleons together.
• Mass defect is the difference between the mass of the nucleus and the sum of the masses of its constituent nucleons.
• Binding energy is the energy required to separate the nucleons in a nucleus.
• Nuclear fission is the splitting of a heavy nucleus into two lighter nuclei.
• Nuclear fusion is the combining of two light nuclei into a heavier nucleus.
• Radioactivity is the spontaneous emission of particles or energy from unstable nuclei.
• Radioactive decay law describes the exponential decay of radioactive substances.

Semiconductor Electronics: Materials, Devices and Simple Circuits

• Semiconductors are materials with electrical conductivity between that of conductors and insulators.
• Intrinsic semiconductors are pure semiconductors with equal concentrations of electrons and holes.
• Extrinsic semiconductors are semiconductors doped with impurities to increase their conductivity.
• n-type semiconductors are doped with donor impurities that contribute extra electrons.
• p-type semiconductors are doped with acceptor impurities that create extra holes.
• p-n junction is formed when a p-type semiconductor is joined with an n-type semiconductor.
• Semiconductor diode is a two-terminal device that allows current to flow easily in one direction but not in the other.
• Rectifier is a circuit that converts AC to DC.
• Transistor is a three-terminal semiconductor device that can be used as an amplifier or a switch.
• Logic gates are electronic circuits that perform logical operations on one or more inputs to produce a single output.