PHYS 219 Recitation

Kevin Ralphs31 Aug 2013

Overview

• HW Questions• Potential Energy• Potential• Capacitors

HW Questions

Ask Away….

Potential Energy• In a closed system with no dissipative forces

• The work done is due to the electric force so

This formula assume the following:• is constant in both magnitude and direction• The displacement is parallel to • 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

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• 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. When possible, we usually choose the potential to be zero very far away

– The potential must be continuous

Tying it Together

Electric Field

Change in Potential

Change in PE

Electric Force

Multiply by q

Multiply by q

Multiply by -Δx Multiply by -Δx

Vectors

Scalars

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

• 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• For parallel plates:

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

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

Capacitance

• A charged capacitor has potential energy

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

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