Electrostatics Fields Refresher Electrical Potential Potential Difference Potential Blame 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 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 You may want to circle it  Units – Convert all units to SI Need to be consistent with k e Need to be consistent with k e

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 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 lines  magnitude 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 Conductor Shielding:

Equipotential Surfaces  Electric Potential is the same at all pts. on surface  W A  D =?  W A  B =?  E field  Equipotentials

Electric Potential Energy  F e is a conservative force (?) F e can make electrical potential energy F e can make electrical potential energy Fe  Work is Independent of Path Fe  Work is Independent of Path  W F e = -  PE

PE from Fields  Compare to Gravity  PE g =ma g d y  PE of earth & mass system  PE e =qEd  PE of q & E field System  PE g = PE go +ma g d y  often choose PE go = 0  PE e =PE eo + qEd

PE from pt Charges 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

Potential Energy & Pt Charges  Sketch the E field vectors inside the capacitor  Sketch the F acting on each charge  Choose a spot for PE e =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  W on q = Fd=qE x  x  ΔPE = - W = - q E x  x = - q E x  x only for a uniform field 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=V B -V A Potential Difference   V=  PE/q   V = qE  d/q   V = E  d + Think about the VanDeGraff demo A B

Electric Potential of a Point Charge  PE e =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 point

Electric Potential of Multiple Point Charges  Superposition principle applies  Is PE e 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 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  V 1 is the electric potential due to q 1 at point P  The work required to bring q 2 from infinity to P without acceleration is q 2 V 1  This work is equal to the potential energy of the two particle system

Problem Solving with Electric Potential (Point Charges)  Draw a diagram of all charges Note the point of interest Note the point of interest  Calculate the distance from each charge to the point of interest  Use the basic equation V = k e q/r Include the sign Include the sign The potential is positive if the charge is positive and negative if the charge is negative 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 Take the algebraic sum  Remember that potential is a scalar quantity So no components to worry about So no components to worry about