ElectrostaticsFields Refresher

Electrical PotentialPotential Difference

PotentialBlame it on the old folks.

Electrical Field

Maxwell developed fields Electric fields exist in the space around

charged objects When other charged object enters this electric

field, the field exerts a force on the second charged object

Problem Solving Strategy

Draw a diagram of the charges in the problem

Identify the charge of interest You may want to circle it

Units – Convert all units to SI Need to be consistent with ke

Electric Field Lines

Electric Field patterns - draw lines in direction of field vector at any point

These are called electric field lines and were introduced by Michael Faraday

Rules for Drawing Electric Field Lines

The lines for a group of charges must begin on positive charges and end on negative charges

In the case of an excess of charge, some lines will begin or end infinitely far away

The number of lines drawn leaving a positive charge or ending on a negative charge is proportional to the magnitude of the charge

No two field lines can cross each other

E Field Lines

Draw E field for a Large Positive Charge Draw E field for small Positive Charge Draw E field for Large Neg Charge Draw E field for small Neg Charge. Draw E Field for a Dipole (1 pos near 1

neg)

Electric Field Line Patterns

Point charge The lines radiate

equally in all directions

For a positive source charge, the lines will radiate outward

Electric Field Line Patterns

For a negative source charge, the lines will point inward

Electric Field Line Patterns

An electric dipole consists of two equal and opposite charges

The high density of lines between the charges indicates the strong electric field in this region

E Fields

Draw E Field for two + Charges

Electric Field Line Patterns

Two equal but like point charges

At a great distance from the charges, the field would be approximately that of a single charge of 2q

The bulging out of the field lines between the charges indicates the repulsion between the charges

The low field lines between the charges indicates a weak field in this region

E Fields

Draw E Fields for Large +Q and small -q

Electric Field Patterns

Unequal and unlike charges

Note that two lines leave the +2q charge for each line that terminates on -q

Fields Refresher

Start on + or inifinity End on – or infinity # field linesmagnitude of

charge or field Dipole = two opposite

charges Fields are everywhere Fields do not affect

everthing.

Fields In Conductors Refresher Equilibrium Conditions: ALL excess charge moves to

outer surface E is zero within the

conductor E on surface MUST be to

surface

E Field in ConductorShielding:

Equipotential Surfaces Electric Potential is

the same at all pts. on surface

WAD=?

WAB =? E field

Equipotentials

Electric Potential Energy

Fe is a conservative force (?) Fe can make electrical potential energy Fe Work is Independent of Path

WFe = - PE

PE from Fields

Compare to Gravity PEg=magdy PE of earth & mass system PEe=qEd PE of q & E field System PEg = PEgo +magdy

often choose PEgo = 0 PEe=PEeo + qEd

PE from pt Charges

qEdPE field q

FE

dq

FqPE echpt arg. 2

21

d

qqkF

d

qkqPE chrgpt

21.

Important Note: This relationship for PE is ONLY for PE due to point charges. THIS DOES NOT WORK FOR FIELDS.

VanDeGraff & Fluorescent Bulb

Potential Energy

qEdPE field

dFW

WPE field

Potential Energy & Pt Charges

Sketch the E field vectors inside the capacitor

Sketch the F acting on each charge

Choose a spot for PEe=0 & Label it.

Is the PE of the + charge +, -, 0

Work and Potential Energy

E is uniform btn plates

q moves from A to B work is done on q Won q = Fd=qEx x ΔPE = - W

= - q Ex x only for a uniform

field

Electric Potential & Pt Charge

In which direction (rt, lft, up, down) does the PE of the + charge decrease? Explain.

In which direction will the + charge move if released from rest? Explain.

Does your last answer agree with the F drawn earlier?

Potential Difference

Voltage = Potential = Electrical Potential V=PE/q V measured in ---? Within E, different PE at Different Pts. V=VB-VA Potential Difference V= PE/q V = qE d/q V = E d

+

Think about the VanDeGraff demo

AB

Electric Potential of a Point Charge

PEe=0 as r The potential created by a point charge q at any

distance r from the charge is

A potential exists w/ or w/o a test charge at that pointr

qkV e

Electric Potential of Multiple Point Charges

Superposition principle applies Is PEe a vector or a scalar? The total electric potential at some point P

due to several point charges is the algebraic/vectoric? sum of the electric potentials due to the individual charges

Energy and Charge Movements, cont

When the electric field is directed downward, point B is at a higher or lower potential? than point A

A positive test charge that moves from A to B gains/loses? electric potential energy

It will gain/lose? the same amount of kinetic energy as it loses in potential energy

Energy and Charge Movements

A positive charge gains electrical potential energy when it is moved in a direction opposite the electric field

If a charge is released in the electric field, it experiences a force and accelerates, gaining kinetic energy

As it gains kinetic energy, it loses an equal amount of electrical potential energy

A negative charge loses electrical potential energy when it moves in the direction opposite the electric field

Potentials in Practice

Rank the points from largest potential (V) to smallest.

Electrical Potential Energy of Two Charges

V1 is the electric potential due to q1 at point P

The work required to bring q2 from infinity to P without acceleration is q2V1

This work is equal to the potential energy of the two particle system

r

qqkVqPE 21

e12

Problem Solving with Electric Potential (Point Charges)

Draw a diagram of all charges Note the point of interest

Calculate the distance from each charge to the point of interest

Use the basic equation V = keq/r Include the sign The potential is positive if the charge is positive and

negative if the charge is negative

Problem Solving with Electric Potential, cont

Use the superposition principle when you have multiple charges Take the algebraic sum

Remember that potential is a scalar quantity So no components to worry about