Download - PHYS 241 Exam 1 Review
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 ways1. Use integration to get the particle’s velocity as a
function of time, then integrate again to gets its position2. Kinematic equations (the result when method 1. is
applied in the case of constant acceleration)
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?– 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
• Electric field due to a point charge at distance r with charge q
• Principle of superposition still applies– You can sum individual fields due to discrete
charges– You can integrate continuous charge distributions
where the charge becomes and the field becomes
Continuous Charge Distributions
• Motivation for the equation:
– Very far from a charge distribution, it looks like a point charge
– So if we “chop” up the distribution into small enough pieces, each one will have a field contribution we can calculate
– The principle of superposition then allows the integrand to approach the true 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 surfaceNote: 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
• 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 allows it
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)
Potential
• Why do I care? (cont.)– If you have the potential defined over a small
area, the potential function encodes the information about the electric field in the derivative
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
• In circuits– In well-behaved configurations, capacitors may
be combined into a single equivalent capacitor– Parallel
* This is like increasing the area of the plates *– Series
* This is like increasing the separation distance *
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
Capacitance
• Capacitors are in equilibrium…– Series: when they have the same charge– Parallel: when they have the same voltage
Practice Problems
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