PHYS 241 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 Electrostatics Coulomb’s Law Principle of Superposition Electric Field Continuous Charge Distributions Conductors vs. Insulators Gauss’s Law Potential Capacitance

Electrostatics Our study of electric fields so far has been based on a few assumptions These assumptions collectively are known as the electrostatic approximation Basically we assume that our systems have to come to a dynamic equilibrium before we do our calculations We will be ignoring transitory behavior or steady state behaviors (no currents or 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 in two ways 1.Use integration to get the particle’s velocity as a function of time, then integrate again to gets its position 2.Kinematic equations (the result when method 1. is applied in the case of constant acceleration)

Coulomb’s Law

Principle of Superposition

Electric Field What does it tell me? – A vector proportional to the force a positive test charge would experience at a point in space Why do I care? – Calculating the force a particular charge feels doesn’t directly tell you how other charges would behave – The electric field gives you a solution that applies to any charge, so it reduces your work

Electric Field

Continuous Charge Distributions

General procedure to setup the integrals – Prepare your integral – Change integral to integrate over where the charge lies (aka parameterization) – Identify elements of the integrand that depend on the integrating variable – Determine explicit relationships with the integrating variable – Integrate

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

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

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

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

Capacitance What does it tell me? – The charge that accumulates on two conductors is proportional to the voltage between them Why do I care? – Capacitors are vital components in electronics – They can be used to temporarily store charge and energy, and play an even more important role when we move to alternating current systems – Camera flashes, touch screen devices, modern keyboards all exploit capacitance

Capacitance

Capacitors are in equilibrium… – Series: when they have the same charge – Parallel: when they have the same voltage

Practice Problems

Practice Problem