PHYS 221 Exam 1 Review Kevin Ralphs. Overview General Exam Strategies Concepts Practice Problems.

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

• Forces have magnitude and direction so Coulomb’s law tells you both of these– Magnitude: – Direction: Along the line connecting the two

bodies. It is repulsive in the case of like charges, attractive for opposite charges

Principle of Superposition

• What does it tell me?– The electric force between two bodies only

depends on the information about those two bodies

• Why do I care?– Essentially, all other charges can be ignored, the

result obtained in pieces and then summed… this is much simpler

Electric Field

• What does it tell me?– The force a positive test charge q 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

Universal

Electric Field

• Electric field at a point due to a point charge at with charge q

k: Coulomb’s Constant

• Principle of superposition still applies– You can sum individual fields due to discrete

charges

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 surfaceNote: 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

• Flux, from the Latin word for “flow,” quantifies the amount of a substance that flows through a surface each second

• It makes sense that we could use the velocity of the substance at each point to calculate the flow

• Obviously we only want the part of the vector normal to the surface, , to contribute because the parallel portion is flowing “along” the surface

• Intuitively then we expect the flux to then be proportional to both the area of the surface and the magnitude of

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

• Your surface must be closed• The charge you use in the formula is the

charge enclosed by your surface• The Gaussian surface need not be a physical

surface• Start from the definition of flux and simplify

only if your surface/field allows it Universal

Potential Energy

• In a closed system with no dissipative forces

• The work done is due to the electric force so

WARNING: Since charge can be negative, and might point in opposite directions (this is called antiparallel) which would change the sign of W

• This can be combined with the work-energy theorem to obtain the velocity a charged particle has after moving through an electric field

Situational:Uniform electricfield and straight path

Situational

Potential

• What does it tell me?– The change in potential energy per unit charge an object

has when moved between two points

• Why do I care?– The energy in a system is preserved unless there is some

kind of dissipative force– So the potential allows you to use all the conservation of

energy tools from previous courses (i.e. quick path to getting the velocity of a particle after it has moved through a potential difference)

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

Charge Force Field PE

Electricity q

Gravity m

Capacitance

• What does it tell me?– The charge that accumulates on two conductors is proportional to

the voltage between them

Q: charge on the capacitor’s plates, C: capacitance, ΔV: potential difference across the capacitor

• 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

• What does capacitance depend on?– Geometry of the plates – Material between the plates– For parallel plates:

C: capacitance, ε: permittivity of the material between the plates, A: area of the plates (may or may not be square), d: distance between the plates

• Unit of capacitance is the Farad– To demystify this, units are (meters*permittivity)

Capacitance

• Dielectric– Put simply, a dielectric is a material (an insulator) that weakens the

electric field around it– This allows more charge to be placed on the plates for the same

voltage (i.e. capacitance is increased)– The permittivity of a dielectric tells you how it affects the

capacitance– The ratio of the permittivity of a dielectric and the permittivity of

free space is the dielectric constant

κ: dielectric constant, ε: permittivity of a material, εo : permittivity of free space,

Cd : capacitance with a uniform dielectric, Cvac: capacitance in the vacuum

Situational:

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 Units SI Units

Length Farads

Length/Charge Volts

Length^2/Charge^2 Newtons

Length/Charge^2 Joules

Practice Problem

Practice Problem

Practice Problem

Practice Problem

Practice Problem

Quiz Questions

Quiz Questions

Quiz Question

Quiz Question