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 Flux Gauss’s Law

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 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 Universal

Electric Field Situational

Continuous Charge Distributions Difficulties in predicting the field due to a continuous charge distribution: – The distribution may have an odd shape – The charge density may change through the distribution This suggests an approach via calculus is appropriate

Continuous Charge Distributions

General procedure to setup the integrals – Write the general integral down – Draw a diagram and label all the parts of the 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, 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 velocity, it looks like this:

Flux

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

Practice Problem