PH2200 Final Exam Study Guide: Electricity, Magnetism, and Waves

SI Prefixes

Understanding SI Prefixes

SI prefixes are used to denote multiples or submultiples of units in the International System of Units (SI). They are essential for expressing very large or very small quantities in physics.

Prefix	Symbol	Factor	Prefix	Symbol	Factor
pico	p	10^{-12}	kilo	k	10^{3}
nano	n	10^{-9}	mega	M	10^{6}
micro	μ	10^{-6}	giga	G	10^{9}
milli	m	10^{-3}	tera	T	10^{12}
centi	c	10^{-2}

Electric Charges and Forces

Charge, Coulomb's Law, and the Electric Field

Electric charge is a fundamental property of matter that causes it to experience a force in an electric field. The force between two point charges is described by Coulomb's Law.

• Elementary Charge (e): The smallest unit of electric charge, $e = 1.602 \times 10^{-19}$ C.

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

• Electric Field (E): The force per unit charge at a point in space: $E = \frac{F}{q}$

• Direction of Electric Field: Away from positive charges, toward negative charges.

Example: Two electrons separated by $1.0 \times 10^{-9}$ m repel each other with a force calculated using Coulomb's Law.

Electric Potential and Potential Energy

Electric Potential (V) and Potential Energy (U)

Electric potential is the electric potential energy per unit charge. It is a scalar quantity and is measured in volts (V).

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

• Potential Difference (Voltage): The work done to move a unit charge between two points: $\Delta V = V_b - V_a = -\int_{a}^{b} \vec{E} \cdot d\vec{s}$

• Potential Energy of a System of Charges: $U = k_e \frac{q_1 q_2}{r}$

Example: The potential energy of three charges at the vertices of an equilateral triangle can be found by summing the potential energy for each pair.

Gauss's Law

Electric Flux and Applications

Gauss's Law relates the electric flux through a closed surface to the charge enclosed by that surface.

• Electric Flux ($\Phi_E$): $\Phi_E = \oint \vec{E} \cdot d\vec{A}$

• Gauss's Law: $\oint \vec{E} \cdot d\vec{A} = \frac{q_{enc}}{\varepsilon_0}$ where $\varepsilon_0 = 8.85 \times 10^{-12}$ C2/N·m2.

• Applications: Used to find electric fields of symmetric charge distributions (spheres, cylinders, planes).

Example: The electric field inside and outside a uniformly charged sphere or cylinder can be found using Gauss's Law.

Capacitance and Dielectrics

Capacitors, Energy Storage, and Dielectric Materials

Capacitors store electric energy in the electric field between their plates. The capacitance depends on the geometry and the dielectric material between the plates.

• Capacitance (C): $C = \frac{Q}{V}$

• Parallel Plate Capacitor: $C = \varepsilon_0 \frac{A}{d}$

• Energy Stored: $U = \frac{1}{2} C V^2$

• Dielectric Constant ($\kappa$): Increases capacitance by a factor $\kappa$.

Example: Calculating the area of plates needed for a given capacitance and voltage.

Current, Resistance, and Circuits

Ohm's Law, Series and Parallel Circuits

Electric current is the flow of charge. Resistance opposes this flow, and Ohm's Law relates current, voltage, and resistance.

• Current (I): $I = \frac{Q}{t}$

• Ohm's Law: $V = IR$

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

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

• Power Dissipated: $P = IV = I^2 R = \frac{V^2}{R}$

Example: Calculating the power dissipated in a resistor connected to a battery.

The Magnetic Field and Electromagnetic Induction

Magnetic Forces, Fields, and Faraday's Law

Magnetic fields exert forces on moving charges and currents. Changing magnetic fields induce electric fields and currents (electromagnetic induction).

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

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

• Faraday's Law of Induction: $\mathcal{E} = -\frac{d\Phi_B}{dt}$

• Lenz's Law: The induced current opposes the change in magnetic flux.

Example: Calculating the induced emf in a loop due to a changing magnetic field.

Electromagnetic Waves and Optics

Wave Properties, Polarization, and the Electromagnetic Spectrum

Electromagnetic waves consist of oscillating electric and magnetic fields. Light can be polarized, and its intensity changes when passing through polarizers.

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

• Frequency and Wavelength: $c = \lambda f$

• Malus's Law (Polarization): $I = I_0 \cos^2 \theta$

Example: Calculating the frequency range of UVA rays given their wavelength range.

Summary Table: Key Equations and Concepts

Concept	Equation	Description
Coulomb's Law	$F = k_e \frac{|q_1 q_2|}{r^2}$	Force between two point charges
Electric Field	$E = \frac{F}{q}$	Force per unit charge
Gauss's Law	$\oint \vec{E} \cdot d\vec{A} = \frac{q_{enc}}{\varepsilon_0}$	Relates electric flux to enclosed charge
Capacitance	$C = \frac{Q}{V}$	Charge stored per unit voltage
Ohm's Law	$V = IR$	Voltage, current, and resistance relationship
Magnetic Force	$\vec{F} = q \vec{v} \times \vec{B}$	Force on a moving charge in a magnetic field
Faraday's Law	$\mathcal{E} = -\frac{d\Phi_B}{dt}$	Induced emf from changing magnetic flux
Speed of Light	$c = \lambda f$	Relationship between speed, wavelength, and frequency

Additional info:

• This study guide covers topics from chapters on electric forces, fields, Gauss's law, potential, capacitance, circuits, magnetism, electromagnetic induction, and waves, as reflected in the PH2200 final exam and formula sheet.

• All equations are provided in standard LaTeX format for clarity and reference.