Final Exam Review Notes

Honors Physics Final Exam Topics

  • Static Electricity

  • Circuits

  • Electromagnetism

  • Circular/Orbital Motion

  • Gas Laws

  • Mathematical Relationships

Electrostatics

Principles

  • Opposite charges attract, like charges repel: This fundamental principle governs the interactions between charged objects. For example, a negatively charged balloon will stick to a positively charged wall.

  • Only electrons can move through a solid due to atomic structure; protons are fixed in the nucleus. Electrons, being much lighter and located in the outer regions of atoms, are more mobile than protons, which are bound within the nucleus. Thus, charge transfer in solids primarily involves electron movement. In materials like semiconductors, however, there can be the concept of 'holes' which act as positive charge carriers. These aren't actual protons moving, but rather the absence of an electron that propagates as a positive charge.

  • Different substances have varying tendencies to gain or lose electrons when rubbed together. This is quantified by the triboelectric series, ranking materials by their ability to become positively or negatively charged. For instance, rubbing fur against Teflon results in Teflon gaining electrons and becoming negatively charged. The further apart two materials are on the triboelectric series, the greater the charge transfer when they are rubbed together. Humidity and surface conditions can affect the amount of charge transferred.

  • Conductors allow electron flow easily due to free electrons; insulators do not, as their electrons are tightly bound to atoms. Metals are good conductors, while rubber and glass are good insulators. Semiconductors have conductivity between conductors and insulators, and their conductivity can be controlled by adding impurities (doping) or by applying an electric field. Superconductors are materials that, below a critical temperature, have zero electrical resistance.

  • Matter allows excess charge to spread out in conductors, while in insulators, charge tends to remain localized. This is why conductors are used to ground electrical equipment, while insulators are used to prevent electrical shocks. In conductors, the free electrons repel each other and move to the surface to maximize the distance between them.

  • Total charge is conserved; it cannot be created or destroyed, only transferred from one object to another. This is a cornerstone of physics. For example, when an object gains electrons, another object must lose the same number of electrons. This is based on the law of conservation of electric charge.

  • Objects tend to be neutral because charged particles redistribute to minimize potential energy. If an object has an excess of charge, it will attract opposite charges to balance it out. This is why neutral objects are attracted to charged objects, as the charges within the neutral object redistribute (polarize) to create an attraction.

Atomic Structure

Components

  • Protons

    • Location: Nucleus

    • Charge: Positive

    • Significance: Determines the element's identity. The number of protons (atomic number) defines what element an atom is.

  • Neutrons

    • Location: Nucleus

    • Charge: Neutral

    • Significance: Contributes to the atom's mass and nuclear stability. Neutrons help to hold the nucleus together by providing strong nuclear force. Isotopes of an element differ in the number of neutrons.

  • Electrons

    • Location: Orbiting the nucleus in specific energy levels or shells

    • Charge: Negative

    • Significance: Involved in chemical bonding and electrical phenomena. Electrons in the outermost shell (valence electrons) determine an atom's chemical properties. The behavior of electrons is governed by quantum mechanics.

    • Net Charge = Number of Protons - Number of Electrons. A positive net charge indicates a deficiency of electrons; a negative net charge indicates an excess. An atom with equal numbers of protons and electrons is electrically neutral. Ions are formed when atoms gain or lose electrons.

    • Atoms become charged by gaining or losing electrons, resulting in ions. Gaining electrons forms anions (negative ions), and losing electrons forms cations (positive ions). For example, sodium (Na) loses an electron to become Na^+, while chlorine (Cl) gains an electron to become Cl^-. Polyatomic ions are groups of atoms that together have a net charge.

    • Mass Number = Number of Protons + Number of Neutrons. This number is crucial for identifying isotopes of an element. Isotopes are atoms of the same element with different numbers of neutrons. Some isotopes are radioactive and decay over time.

Electrostatic Phenomena

  • Charging by Friction / Triboelectric Charging

    • Two substances rubbed together transfer electrons based on their electron affinity. The triboelectric series lists materials in order of their tendency to gain or lose electrons. When you rub a balloon on your hair, electrons are transferred from your hair to the balloon, making the balloon negatively charged. The amount of charge transferred depends on the materials, the pressure, and the speed of rubbing. Static cling in clothes is another example of triboelectric charging.

  • Conduction

    • Transferring charge between objects through direct contact. Effective charge transfer requires a conductive path. Touching a charged metal rod will transfer charge to you if you are grounded. The rate of charge transfer depends on the voltage difference and the resistance of the path. Sparking is a rapid discharge of static electricity through air.

  • Grounding

    • Connecting an object to the Earth to neutralize it by allowing electrons to flow in or out. This is essential for safety in electrical systems, preventing charge buildup. Grounding a metal appliance casing prevents electric shock if a wire comes loose and touches the casing. The Earth acts as a large reservoir of charge, able to accept or donate electrons without significantly changing its own potential.

  • Polarization

    • Redistribution of charge within a neutral conductor when a charged object is brought nearby. No net charge is created; charges simply separate. A charged rod brought near a neutral metal sphere will cause the electrons in the sphere to redistribute, creating a temporary dipole. This polarization is why a charged object can attract a neutral object.

  • Induced Charge

    • When a charged object is brought near a neutral object, it can induce a charge separation in the neutral object. This occurs because the charges in the neutral object are either attracted to or repelled by the charged object, causing them to redistribute. An example is when a charged comb attracts small pieces of paper.

  • Electrostatic Force (Coulomb's Law)

    • The force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The force is attractive if the charges are opposite and repulsive if the charges are the same. The mathematical representation is F=k\frac{|q1q2|}{r^2}, where F is the force, k is Coulomb's constant (8.99x10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the separation distance.

  • Modeling Electrostatic Events: Rubbing a Plastic Ruler

    • Rubbing the Plastic Ruler with Rabbit Fur: This is triboelectric charging. Electrons are transferred from the rabbit fur to the plastic ruler (assuming plastic has a higher electron affinity), making the ruler negatively charged and the fur positively charged. The amount of charge transferred depends on the materials and the conditions

    • Bringing the Ruler Near the Foil Bit (Without Touching): This is charging by induction. The negatively charged ruler repels electrons in the foil bit, causing them to move away from the ruler. This leaves the side of the foil bit closer to the ruler with a net positive charge, while the side farther away has a net negative charge. The foil bit is polarized, and there is an attractive force between the ruler and the foil, but they haven't actually exchanged any charge.

    • Touching the Foil Bit with the Ruler: This is charging by conduction. Some of the excess electrons on the negatively charged ruler will now flow onto the foil bit. Now, the foil bit has a net negative charge. The ruler and the foil bit repel each other because they have the same type of charge.

    • Grounding the Foil Bit with a Paper Clip: The negatively charged foil bit is connected to the Earth (ground) via the paper clip. The Earth is a very large reservoir for charge and can effectively neutralize the charge on the foil bit. Excess electrons in the foil bit flow through the paper clip to the ground, until the foil bit is neutral

Circuits

  • Voltage (V)

    • Electric potential energy difference between two points, measured in volts. Voltage drives the flow of current in a circuit. Voltage is analogous to pressure in a water pipe.

    • Acts as an electron pump, providing the energy for electrons to move. A battery is a common source of voltage in a circuit.

    • Can be produced by batteries (chemical energy to electrical energy) or generators (mechanical energy to electrical energy). Solar cells can also produce voltage by converting light energy into electrical energy.

  • Current (I)

    • Flow of electrons, measured in Amperes (A). Current is the rate at which charge flows through a conductor. Current is analogous to the flow rate of water in a pipe.

    • 1 Amp = 6,250,000,000,000,000,000 electrons per second. A large number of electrons must move together to produce a measurable current. This number is derived from the charge of a single electron (1.602x10^{-19} Coulombs) and the definition of an Ampere (1 Coulomb per second).

    • Example currents: microwave (10 A), vacuum cleaner/hair dryer (12 A), 60-Watt bulb (0.5 A). These values give a sense of the current requirements for common appliances. High-current appliances require thicker wires to prevent overheating.

  • Resistance (R)

    • Opposition to current flow, measured in Ohms (Ω). Resistance converts electrical energy into heat. Resistance is analogous to a narrow section in a water pipe that restricts water flow.

    • Conductors have low resistance, allowing easy current flow; insulators have high resistance, impeding current flow. Copper wire has low resistance, while a rubber band has high resistance.

  • Ohm’s Law

    • V=IR. This law relates voltage, current, and resistance in a circuit. This is a fundamental law in circuit analysis.

    • Can be used to find voltage, current, and resistance in a circuit if two of the values are known. This is a fundamental tool for circuit analysis. If you know the voltage and current in a circuit, you can calculate the resistance using Ohm's Law: R=V/I

  • Power (P)

    • Determines the brightness of a lightbulb, measured in Watts (W). Power is the rate at which electrical energy is converted into another form (e.g., light or heat). A higher wattage bulb will produce more light (and heat) than a lower wattage bulb.

    • P=IV

Electromagnetism

  • Magnetic fields are caused by MOVING CHARGES. This is a fundamental principle linking electricity and magnetism. This is why electric currents create magnetic fields.

  • Electrons spinning create magnetic fields. The intrinsic angular momentum (spin) of electrons gives rise to magnetic dipole moments. Unpaired electrons contribute to a material's magnetism.

  • Magnetic Domains

    • A domain is defined as a cluster of atoms that are arranged the same way/direction. In ferromagnetic materials, these domains can align, leading to a strong net magnetic field. When these domains are aligned, the material becomes magnetized.

  • Ferromagnetic Materials

    • Can be magnetized, e.g., Iron, Nickel, Cobalt. These materials have unpaired electron spins that align spontaneously. These materials are used in making permanent magnets.

  • Fields

    • Region around a magnetic material or a moving electric charge within which the force of magnetism acts. Magnetic fields exert forces on other magnetic materials or moving charges. Magnetic fields are vector quantities, having both magnitude and direction.

  • Compasses

    • A compass is a small, pointed magnet that can rotate freely. The Earth itself has a magnetic field, which aligns compass needles. The Earth's magnetic field is generated by the movement of molten iron in its core.

    • The compass enables us to know what direction we are traveling, because the needle’s magnetism interacts with the Earth Magnetism

  • Magnetic field lines begin at N pole and end at S pole, field exists inside the magnet pointing from S to N. These lines are a visual representation of the magnetic field.

  • Like poles repel, opposite poles attract. This is a fundamental property of magnets. This is why two north poles will push away from each other, while a north and south pole will pull towards each other.

  • The strength of the magnetic field is indicated by how close the lines are to each other. The closer the lines, the stronger the magnetic field.

Current and Magnetic Fields

  • Moving electrons (current) create magnetic fields. This is the basis for electromagnets and electric motors. The strength of the magnetic field is proportional to the current.

  • Right Hand Rule #1. Used to determine the direction of the magnetic field around a current-carrying wire. Point your thumb in the direction of the current, and your fingers will curl in the direction of the magnetic field.

  • Right Hand Rule #2. Used to determine the direction of the force on a current-carrying wire in a magnetic field. Point your fingers in the direction of the magnetic field, your thumb in the direction of the current, and your palm will face the direction of the force.

  • Right Hand Rule #3. Used to determine the direction of the magnetic field inside a solenoid. Curl your fingers in the direction of the current, and your thumb will point in the direction of the magnetic field inside the solenoid.

  • Towards = “out of the paper”. Convention for representing vectors perpendicular to the page. This is often represented by a dot inside a circle (⊙).

  • Away = “into the paper”. Convention for representing vectors perpendicular to the page. This is often represented by a cross inside a circle (⊗).

Motors

  • Convert electrical energy into mechanical energy using interactions between magnetic fields and electric current. Motors utilize the force on current-carrying wires in a magnetic field to produce rotational motion. Electric motors are used in countless applications, from electric cars to power tools.

Electromagnets

  • Electric current produces a magnetic field. The strength of the magnetic field is proportional to the current. This principle is used in electromagnets to create controllable magnetic fields.

  • Looping wire with current around a ferromagnetic material creates a strong magnet. The ferromagnetic core enhances the magnetic field. This is how electromagnets can lift heavy objects.

  • Composed of a battery, wire loops, and a ferromagnetic core (iron, cobalt, nickel). The battery provides the current, the wire loops create the magnetic field, and the core concentrates it. The more loops of wire, the stronger the electromagnet.

  • Can be turned on/off, strength can be modified by coils, spacing, current, and core material. More coils, closer spacing, higher current, and a more permeable core material all increase the strength. Electromagnets are used in MRI machines, particle accelerators, and many other scientific and industrial applications.

Circular/Orbital Motion

  • Uniform Circular Motion (UCM)

    • Movement along a circular path with constant speed. The object's speed remains constant, but its velocity changes due to the changing direction. A satellite orbiting the Earth at a constant speed is an example of UCM.

    • Velocity is tangent to orbit, acceleration and net force point inward. This inward acceleration is called centripetal acceleration. Without this acceleration, the object would move in a straight line.

    • Equation: a=\frac{v^2}{r}

    • a= acceleration

    • v= velocity

    • r= radius

    • Mass only affects net force, speed and radius affect acceleration and net force. Higher speeds and smaller radii require greater centripetal force. A more massive object requires a greater centripetal force to maintain the same circular motion.

  • Elliptical Circular Motion (ECM)

    • Speed and force are not constant. Kepler's laws describe the motion in such orbits. Planets in our solar system follow elliptical orbits.

    • Velocity is tangent to orbit, and acceleration is not perpendicular to velocity. The acceleration has both radial and tangential components. This tangential component causes the object to speed up or slow down.

    • Velocity and Force increase when near the object its orbiting and decrease when far away from the object. This is due to the conservation of angular momentum. A planet moves faster when it is closer to the sun and slower when it is farther away.

Kepler’s Laws

  • First Law: Planets orbit in an ellipse with the sun at one focus. The ellipse's shape is defined by its semi-major axis and eccentricity. The eccentricity of an ellipse determines how elongated it is.

  • Second Law: Planets sweep out equal areas in equal times; speed varies in orbit, faster near the sun. This is a consequence of the conservation of angular momentum. A planet covers more distance in a given time when it is closer to the sun.

  • Third Law: Orbital period increases with orbital radius. This relates the orbital period to the size of the orbit. Planets that are farther from the sun take longer to orbit.

Forces in Simulation

  • Inward force: gravity, outward force: centripetal force. Gravity provides the centripetal force necessary for orbit. The balance between gravity and inertia keeps an object in orbit.

  • Equation: G\frac{m{sun}m{earth}}{r^2} = \frac{m_{earth}v^2}{r}

    • G= 6.67x10^{-11}

  • Simplified equation: v = \sqrt{\frac{Gm}{r}}

  • Speed depends on the mass of the central object and radius. Larger central mass and smaller radius lead to higher orbital speeds. A satellite orbiting a more massive planet will have a higher orbital speed.

Ideal Gas Law

  • Equation: PV=nRT

    • P= pressure in atm or Pascals

    • V= volume in liters (1 L= 1 meter3)

    • n= moles or amount of the gas

    • R= constant, 8.314 J/mol K

    • T= temperature in Kelvin (K) (273K = 1℃)

  • Variables on the same side of the equation are inversely related. For example, at constant temperature, increasing pressure decreases volume. This is why compressing a gas