Physics Study Guide: Electricity, Magnetism, Waves, Quantum, Atomic, and Nuclear Physics

Chapter 19: Electric Charges, Forces, and Fields

Coulomb Force and Coulomb’s Law

The Coulomb force describes the interaction between two point charges. It is governed by Coulomb’s Law, which quantifies the magnitude and direction of the force.

• Coulomb’s Law: The force between two point charges $q_1$ and $q_2$ separated by distance $r$ is given by: $F = k_e \frac{|q_1 q_2|}{r^2}$ where $k_e$ is the electrostatic constant ($k_e = 8.99 \times 10^9$ N·m2/C2).

• Vector Addition: Multiple forces can be added using vector addition.

Electric Field and Electric Field Lines

An electric field is a region where a charge experiences a force. Electric field lines visually represent the direction and strength of the field.

• Electric Field of a Point Charge: $E = k_e \frac{|q|}{r^2}$

• Superposition Principle: Electric fields from multiple charges add vectorially.

• Test Charge: A hypothetical charge used to measure the field without affecting it.

• Field Line Properties:

  • Start on positive charges, end on negative charges.

  • Density of lines indicates field strength.

• Force and Electric Field Relationship: $\vec{F} = q \vec{E}$

Chapter 20: Electric Potential & Electric Potential Energy

Electric Potential Energy vs Electric Potential (Voltage)

Electric potential energy is the energy a charge has due to its position in an electric field. Electric potential (voltage) is the energy per unit charge.

• Electric Potential: $V = k_e \frac{q}{r}$

• Conservation of Energy: Changes in potential energy relate to work done by the field.

• Adding Potentials: Electric potentials are scalars and can be summed directly.

• Charge Movement: Positive charges move from high to low potential; negative charges move from low to high potential.

• Equipotential: A surface where the potential is constant.

Capacitance

Capacitance measures a system’s ability to store charge per unit voltage.

• Capacitance Formula: $C = \frac{Q}{V}$

Chapter 21: Electric Current & Direct-Current Circuits

Electric Current and Resistance

Electric current is the flow of charge; resistance opposes this flow.

• Current: $I = \frac{Q}{t}$

• Ohm’s Law: $V = IR$

• Electrical Power: $P = IV$

Series and Parallel Circuits

• Resistors in Series: $R_{\text{total}} = R_1 + R_2 + \ldots$

• Resistors in Parallel: $\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots$

• Capacitors in Series: $\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \ldots$

• Capacitors in Parallel: $C_{\text{total}} = C_1 + C_2 + \ldots$

Chapter 22: Magnetism

Magnetic Fields and Forces

A magnetic field exerts a force on moving charges.

• Magnetic Force: $\vec{F} = q \vec{v} \times \vec{B}$

• Right Hand Rule: Used to determine the direction of force on a positive charge.

• Radius of Charged Particle Path: $r = \frac{mv}{qB}$

• Magnetic Field from a Long, Straight Wire: $B = \frac{\mu_0 I}{2\pi r}$

Chapter 25: Electromagnetic Waves

Production and Properties of Electromagnetic Waves

Electromagnetic waves are produced by accelerating charges and propagate at the speed of light in vacuum.

• Speed of Light: $c = 3.00 \times 10^8$ m/s

• Doppler Effect: Change in frequency due to relative motion.

• Wave Speed Relation: $v = f \lambda$

• Energy of a Photon: $E = hf$

• Intensity: Power per unit area.

• Polarization: Orientation of the electric field vector.

• Malus’ Law: $I = I_0 \cos^2 \theta$

Chapter 26: Geometric Optics

Reflection and Refraction

Light interacts with surfaces via reflection and refraction, governed by physical laws.

• Law of Reflection: Angle of incidence equals angle of reflection.

• Plane Mirror Images: Images are virtual, upright, and same size as object.

• Refraction: Bending of light as it passes between media.

• Snell’s Law: $n_1 \sin \theta_1 = n_2 \sin \theta_2$

• Index of Refraction: $n = \frac{c}{v}$

• Critical Angle: $\theta_c = \sin^{-1} \left( \frac{n_2}{n_1} \right)$

• Total Internal Reflection: Occurs when light cannot exit a medium.

• Brewster’s Angle: $\theta_B = \tan^{-1} \left( \frac{n_2}{n_1} \right)$

• Dispersion: Separation of light into colors due to varying refractive indices.

Chapter 28: Physics Optics: Interference and Diffraction

Interference and Diffraction

Interference and diffraction arise from the superposition of waves.

• Constructive Interference: Occurs when path difference is a multiple of wavelength.

• Destructive Interference: Occurs when path difference is a half-integer multiple of wavelength.

• Path Length Difference: $\Delta L = m \lambda$ (constructive), $\Delta L = (m + 0.5) \lambda$ (destructive)

• Interference/Diffraction Pattern Indexing: Assigning order numbers to maxima/minima.

• Double Slit Spacing: $d \sin \theta = m \lambda$

• Single Slit Width: $a \sin \theta = m \lambda$

• Phase Change on Reflection: $\pi$ phase shift occurs when reflecting from a medium of higher refractive index.

• Thin Film Interference: Minimum thickness for constructive interference: $t = \frac{m \lambda}{2n}$

Chapter 30: Quantum Physics

Quantum Properties of Light and Matter

Quantum physics describes the discrete nature of energy and matter.

• Wien’s Displacement Law: $\lambda_{\text{max}} = \frac{b}{T}$, where $b = 2.898 \times 10^{-3}$ m·K

• Photon Energy: $E = hf$

• Photoelectric Effect: Electrons are emitted when light exceeds cutoff frequency.

• Cutoff Frequency: $f_c = \frac{\phi}{h}$

• Photon Momentum: $p = \frac{E}{c} = \frac{hf}{c}$

• Compton Scattering: Change in wavelength: $\Delta \lambda = \lambda' - \lambda = \frac{h}{m_e c}(1 - \cos \theta)$

• De Broglie Wavelength: $\lambda = \frac{h}{p}$

Chapter 31: Atomic Physics

Bohr Model and Spectral Lines

The Bohr model explains atomic structure and spectral lines for hydrogen.

• Hydrogen Spectral Lines: $\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$, $R$ is the Rydberg constant.

• Bohr Orbit Radius: $r_n = n^2 a_0$, $a_0$ is the Bohr radius.

• Total Energy: $E_n = - \frac{13.6}{n^2}$ eV

• Electron Momentum: $p_n = \frac{h}{2\pi r_n}$

• Angular Momentum: $L_n = n \hbar$

• Quantum Numbers: Describe electron state (n, l, ml, ms).

• K-shell Transition Energy: Energy difference between n=1 and higher levels.

Chapter 32: Nuclear Physics and Nuclear Radiation

Nuclear Structure and Decay

Nuclei are characterized by their composition and undergo various decay processes.

• Nucleus Notation: $^{A}_{Z}X$

• Alpha Decay: Emission of $^4_2He$

• Beta Decay: Emission of electron or positron

• Gamma Decay: Emission of high-energy photon

• Penetrating Abilities: Gamma > Beta > Alpha

• Shielding: Lead for gamma, plastic for beta, paper for alpha

• Photon Transmission: Attenuation as photons pass through matter

• Activity: Number of decays per second (Becquerel, Curie)

Exponential Decay and Nuclear Processes

• Exponential Decay: $N(t) = N_0 e^{-\lambda t}$

• Decay Constant: $\lambda$ is the probability per unit time

• Half-life: $t_{1/2} = \frac{\ln 2}{\lambda}$

• Activity as Function of Time: $A(t) = \lambda N(t)$

• Nuclear Fission: Splitting heavy nuclei

• Nuclear Fusion: Combining light nuclei

Radiation Units and Biological Effects

• Roentgen: Unit of exposure

• Relative Biological Effectiveness (RBE): Factor for biological damage

• Roentgen Equivalent Man (rem): $\text{rem} = \text{rad} \times \text{RBE}$

Type of Radiation	Particle	Penetration	Shielding
Alpha	$^4_2He$	Low	Paper
Beta	Electron/Positron	Medium	Plastic
Gamma	Photon	High	Lead