PHYS 221 Exam 1 Review Kevin Ralphs

Overview General Exam Strategies Concepts Practice Problems

General Exam Strategies Don’t panic!!! If you are stuck, move on to a different problem to build confidence and momentum Begin by drawing free body diagrams “Play” around with the problem Take fifteen to twenty minutes before the exam to relax… no studying. Look for symmetries

Concepts Electricity – Electrostatics – Coulomb’s Law – Principle of Superposition – Electric Field – Conductors vs. Insulators – Flux – Gauss’s Law – Potential Energy – Potential – Capacitance

Concepts Circuits – Current – Resistance/Resistivity – Kirchoff’s Rules Magnetism – Magnetic Fields

Electrostatics It may not have been explicit at this point, but we have been operating under some assumptions We have assumed that all of our charges are either stationary or in a state of dynamic equilibrium We do this because it simplifies the electric fields we are dealing with and eliminates the presence of magnetic fields

Coulomb’s Law What does it tell me? – It tells you the force between two charged particles Why do I care? – Forces describe the acceleration a body undergoes – The actual path the body takes in time can be found from the acceleration using kinematics if the acceleration is uniform

Coulomb’s Law

Principle of Superposition

Electric Field Universal

Electric Field Situational

Conductors vs Insulators Conductors – All charge resides on the surface, spread out to reduce the energy of the configuration – The electric field inside is zero – The potential on a conductor is constant (i.e. the conductor is an equipotential) – The electric field near the surface is perpendicular to the surface Note: These are all logically equivalent statements, but only apply in the electrostatic approximation

Conductors vs Insulators Insulators – Charge may reside anywhere within the volume or on the surface and it will not move – Electric fields are often non-zero inside so the potential is changing throughout – Electric fields can make any angle with the surface

Flux

For the case of a flat surface and uniform electric field, it looks like this:

Gauss’s Law What does it tell me? – The electric flux (flow) through a closed surface is proportional to the enclosed charge Why do I care? – You can use this to determine the magnitude of the electric field in highly symmetric instances – Flux through a closed surface and enclosed charge are easily exchanged

3 Considerations for Gaussian Surfaces Gauss’s law is true for any imaginary, closed surface and any charge distribution no matter how bizarre. It may not be useful, however. 1.The point you are evaluating the electric field at needs to be on your surface 2.Choose a surface that cuts perpendicularly to the electric field (i.e. an equipotential surface) 3.Choose a surface where the field is constant on the surface *Note this requires an idea of what the field should look like

Common Gauss’s Law Pitfalls Universal

Potential Energy Situational: Uniform electric field and straight path Situational

Potential Situational: Electrostatics

Potential Word of caution: – Potential is not the same as potential energy, but they are intimately related – Electrostatic potential energy is not the same as potential energy of a particle. The former is the work to construct the entire configuration, while the later is the work required to bring that one particle in from infinity – There is no physical meaning to a potential, only difference in potential matter. This means that you can assign any point as a reference point for the potential – The potential must be continuous

Analogies with Gravity Electricity and magnetism can feel very abstract because we don’t usually recognize how much we interact with these forces There are many similarities between gravitational and electric forces The major difference is that the electric force can be repulsive Gravity even has a version of Gauss’s law ChargeForceFieldPE Electricityq Gravitym

Capacitance

Situational: Assumes steady fields Assumes uniform dielectric

Capacitance The permittivity of free space has no physical meaning It merely changes physical quantities into their appropriate SI units Physical UnitsSI Units LengthFarads Length/ChargeVolts Length^2/Charge^2Newtons Length/Charge^2Joules

Practice Problem

Quiz Questions

Quiz Question