II PUC Physics Concepts Flashcards

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Electric field

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The electric field at a point is the force experienced per unit positive test charge placed at that point. It is a vector quantity given by $\mathbf{E}=\dfrac{\mathbf{F}}{q_0}$ where $\mathbf{F}$ is the force on test charge $q_0$. The field of a point charge points radially and falls off as $1/r^2$.

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Source charge

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A source charge is any charge that produces an electric field in the surrounding space. It is distinct from the test charge used to probe the field and is responsible for the field distribution. The sign and magnitude of the source charge determine the field direction and strength.

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Electric potential

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Electric potential at a point is the work done per unit charge to bring a test charge from infinity to that point without acceleration. For a point charge $q$ it is given by $V=\dfrac{q}{4\pi\epsilon_0 r}$ and its sign follows the sign of $q$. Potential is a scalar quantity.

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Electric flux

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Electric flux through a closed surface equals the net charge enclosed divided by the permittivity, according to Gauss's law. Mathematically, $\Phi_E=\dfrac{q_{\text{enc}}}{\epsilon_0}$. Flux is a scalar measure of field lines penetrating a surface.

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Torque on dipole

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An electric dipole of moment $\mathbf{p}$ in a uniform electric field $\mathbf{E}$ experiences a torque given by $\boldsymbol{\tau}=\mathbf{p}\times\mathbf{E}$. The torque tends to align the dipole with the field and its magnitude is $\tau=pE\sin\theta$ where $\theta$ is the angle between $\mathbf{p}$ and $\mathbf{E}$. No net force acts on the dipole in a uniform field.

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Parallel plate capacitance

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The capacitance of a parallel-plate capacitor depends on plate area $A$, separation $d$, and dielectric constant $K$ (relative permittivity). It is given by $C=\dfrac{\epsilon_0 K A}{d}$. Larger area or higher $K$ increases capacitance while larger separation reduces it.

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Conductivity

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Electrical conductivity $\sigma$ of a material relates current density to electric field via $\mathbf{j}=\sigma\mathbf{E}$. For a metal with free electron density $n$, charge $e$, relaxation time $\tau$ and mass $m$, $\displaystyle \sigma=\dfrac{ne^2\tau}{m}$. Higher $n$ or longer $\tau$ increases conductivity.

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Mobility

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Mobility $\mu$ of charge carriers is the ratio of drift velocity to applied electric field and for electrons is $\mu=\dfrac{e\tau}{m}$. It quantifies how quickly carriers respond to an electric field and depends on relaxation time $\tau$ and carrier mass $m$. Higher mobility yields larger currents for a given field.

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Magnetic field lines

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Magnetic field lines are closed loops that indicate the direction of the magnetic field at every point; their tangent gives the field direction. They never intersect, are denser where the field is stronger, and emerge from north poles and enter south poles of magnets. They provide a qualitative picture of magnetic field geometry.

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Biot–Savart law

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The Biot–Savart law gives the magnetic field $d\mathbf{B}$ due to a small current element $I\,d\mathbf{l}$ as $d\mathbf{B}=\dfrac{\mu_0}{4\pi}\dfrac{I\,d\mathbf{l}\times\hat{r}}{r^2}$. Integrating over a current distribution yields the total magnetic field. It is used to derive the axial field of a circular loop and other steady-current fields.

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Loop axial field

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The magnetic field on the axis of a circular loop of radius $r$ carrying current $I$ at a distance $x$ from the center is $\displaystyle B=\dfrac{\mu_0 I r^2}{2\left(r^2+x^2\right)^{3/2}}$. The field is maximum at the center ($x=0$) where $B=\dfrac{\mu_0 I}{2r}$. The direction follows the right-hand rule.

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de Broglie wavelength

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The de Broglie hypothesis assigns a wavelength to a particle of momentum $p$ given by $\lambda=\dfrac{h}{p}=\dfrac{h}{mv}$. Matter waves demonstrate wave–particle duality and were confirmed by electron diffraction experiments. Shorter wavelengths correspond to higher momenta.

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Photoelectric slope

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In the photoelectric effect, the stopping potential $V_s$ plotted versus frequency $f$ is linear with slope $\dfrac{h}{e}$ according to $V_s=\dfrac{h}{e}f-\dfrac{\phi}{e}$. Here $h$ is Planck's constant, $e$ the electron charge and $\phi$ the work function. This relation confirms the particle nature of light.

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Half-wave rectifier

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A half-wave rectifier allows current through a load during only one half-cycle of the AC input using a single diode, producing a pulsating DC output. During the positive half-cycle the diode conducts; during the negative half-cycle it is reverse biased and blocks current. The output is unidirectional but has large ripple unless filtered.

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Resonance frequency

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The resonance (angular) frequency of a series LCR circuit is independent of resistance and given by $\omega_0=\dfrac{1}{\sqrt{LC}}$, where $L$ and $C$ are inductance and capacitance. At resonance the impedance is minimum and the circuit current is maximum for a given voltage. Damping due to $R$ affects bandwidth but not $\omega_0$.

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Magnetic susceptibility

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Magnetic susceptibility is a measure of how a material becomes magnetized in an applied magnetic field and differs by type: diamagnetic materials have small negative susceptibility, paramagnetic small positive susceptibility, and ferromagnetic materials large positive susceptibility. These values reflect underlying atomic and domain behaviors. Susceptibility determines how materials respond to external fields.

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Coulomb's law

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Coulomb's law states that the electrostatic force between two point charges is along the line joining them and has magnitude $F=\dfrac{1}{4\pi\epsilon_0}\dfrac{|q_1 q_2|}{r^2}$. In vector form $\mathbf{F}=\dfrac{1}{4\pi\epsilon_0}\dfrac{q_1 q_2}{r^2}\hat{r}$. It expresses the inverse-square dependence of electrostatic forces.

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SI unit charge

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The SI unit of electric charge is the coulomb (C). One coulomb is defined as the amount of charge which, when placed 1 m apart from an equal charge in vacuum, repels it with a force of $9\times10^9\,$N. Charges are quantized in integer multiples of the elementary charge $e\approx1.6\times10^{-19}\,$C.

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Ohm's law

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Ohm's law states that the current through a conductor is directly proportional to the potential difference across it provided temperature and physical conditions remain constant. It is expressed as $V=IR$, where $R$ is the resistance. This linear relation holds for ohmic materials.

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Lorentz force

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The Lorentz force on a charge $q$ moving with velocity $\mathbf{v}$ in electric and magnetic fields is $\mathbf{F}=q\left(\mathbf{E}+\mathbf{v}\times\mathbf{B}\right)$. The electric part acts regardless of motion while the magnetic part acts perpendicular to velocity, doing no work. This law governs charged-particle motion in EM fields.

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Ampere–Maxwell law

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Ampere–Maxwell law extends Ampere's law by including displacement current and in integral form is $\displaystyle \oint\mathbf{B}\cdot d\mathbf{l}=\mu_0\left(I_{\text{cond}}+\epsilon_0\dfrac{d\Phi_E}{dt}\right)$. The $\epsilon_0\dfrac{d\Phi_E}{dt}$ term ensures consistency with charge conservation and predicts electromagnetic waves. It couples time-varying electric fields to magnetic fields.

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Displacement current

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Displacement current is an effective current term arising from a time-varying electric field and is given by $I_D=\epsilon_0\dfrac{d\Phi_E}{dt}$. It allows Ampere's law to hold for time-dependent situations and completes Maxwell's equations. It does not involve physical charge motion but produces magnetic effects equivalent to a real current.

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Impact parameter

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The impact parameter is the perpendicular distance between the initial velocity vector of a projectile (like an $\alpha$-particle) and the center of the target nucleus when far away. It determines the scattering angle in Coulomb scattering; a zero impact parameter corresponds to head-on collision producing maximum deflection. It is a key quantity in Rutherford scattering analysis.

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Conductors (electrostatics)

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In electrostatic equilibrium a conductor has zero electric field inside, excess charge resides only on its outer surface, and the potential is constant throughout the conductor and on its surface. The electric field at the surface is normal to the surface and proportional to surface charge density. These results follow from charge mobility and Gauss's law.

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Magnetic dipole torque

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A current loop with magnetic dipole moment $\mathbf{m}$ in a magnetic field $\mathbf{B}$ experiences a torque $\boldsymbol{\tau}=\mathbf{m}\times\mathbf{B}$. The torque tends to align the dipole moment with the magnetic field and has magnitude $\tau=mB\sin\theta$. This is analogous to electric dipole torque in an electric field.

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Self-inductance factors

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Self-inductance of a solenoid depends on its number of turns, cross-sectional area, length, and the relative permeability of the core material. Larger turns, greater area, shorter length, or higher permeability increase inductance. These parameters determine how much magnetic flux links per unit current.

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Magnetic energy

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Energy stored in an inductor of inductance $L$ carrying current $I$ is $\displaystyle U=\tfrac{1}{2}LI^2$. This energy is stored in the magnetic field produced by the current and equals the work done against the induced emf while building up the current. It is recoverable if the current is later reduced.

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Snell's law

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Snell's law relates angles of incidence $i$ and refraction $r$ across an interface: $n_1\sin i=n_2\sin r$, where $n_1$ and $n_2$ are refractive indices. It follows from Huygens' principle by matching phase fronts across the boundary. The law governs refraction behavior between media.

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Photoelectric work function

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The work function $\phi$ is the minimum energy required to remove an electron from a metal surface. Electrons are emitted only if incident photon energy $hf$ exceeds $\phi$, and the maximum kinetic energy is $K_{\max}=hf-\phi$. The work function is a material property.

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Diffraction reason

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Diffraction of waves is significant when obstacle or aperture dimensions are comparable to the wavelength; for light the wavelength is very small relative to everyday objects so diffraction effects are typically small. This explains why we do not commonly observe light diffraction in macroscopic scenes. Diffraction demonstrates wave nature and affects resolution.

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Paramagnetism

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Paramagnetism is a magnetic behavior in which unpaired atomic magnetic moments align weakly with an external field, producing a small positive susceptibility. Paramagnetic materials are attracted to magnetic fields but do not retain magnetization when the field is removed. The effect arises from permanent atomic magnetic moments.

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Diamagnetism

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Diamagnetism is a universal property where materials develop an induced magnetic moment opposite to an applied magnetic field, giving a small negative susceptibility. It is a weak effect arising from changes in orbital motion of electrons and is present in all materials though often masked by stronger magnetism. Diamagnetic materials are weakly repelled by magnetic fields.

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Isobars

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Isobars are nuclides having the same mass number (total number of nucleons) but different atomic numbers. For example, nuclei with mass number $A$ but different proton counts are isobars. Chemical properties differ while mass number remains same.

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Isotones

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Isotones are nuclei having the same number of neutrons but different numbers of protons and hence different mass numbers. They share neutron count and can exhibit different chemical behavior due to differing proton number. Isotone identification is useful in nuclear reaction analyses.

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Nuclear fission

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Nuclear fission is the splitting of a heavy nucleus into two lighter nuclei accompanied by release of energy, often initiated by a projectile neutron. Fission yields significant energy per reaction and can be controlled in reactors but produces radioactive waste. It usually requires no extremely high temperature to proceed once initiated.

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Nuclear fusion

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Nuclear fusion is the process by which two light nuclei combine to form a heavier nucleus, releasing large amounts of energy per unit mass. Fusion reactions require extremely high temperatures to overcome Coulomb repulsion and are cleaner with less radioactive waste than fission, but are difficult to control presently. Fusion powers stars.