Physics 1202: Lecture 4 Today’s Agenda Announcements: –Lectures posted on: –HW assignments, solutions etc. Homework #1:Homework #1: –On Masterphysics: due this coming Friday –Go to masteringphysics.com and register –Course ID: MPCOTE62465 Labs: Begin next week

Today’s Topic : Chapter 16: Electric energy & potential –Definition –How to compute them –Point charges –Capacitors

Electric potential Energy Recall 1201 Total mechanical energy –Constant for conservative forces Potential energy U –Depends only on position (ex: U = mgy) –Change in U is independent of path kinetic potential U 2, y 2 U 1, y 1

Electric potential Energy Gravitational force (magnitude) Gravitational Potential energy U By analogy: Electric force Electric potential energy 

Electric potential Energy Meaning: recall Total energy is conserved –Variation of U with r  variation of kinetic energy For multiple charges –Simple sum –Ex: 3 charges q1q1 q3q3 q2q2 r 13 r 12 r 23

Lightning

Energy Units MKS: U = QV  1 coulomb-volt = 1 joule for particles (e, p,...) 1 eV = 1.6x joules Accelerators Electrostatic: VandeGraaff electrons  100 keV ( 10 5 eV) Electromagnetic: Fermilab protons  1TeV ( eV)

Electric Potential q A C B r A B r path independence equipotentials R R Rr V Q 4   r Q 4   R

Electric Potential By analogy with the electric field Defined using a test charge q 0 We define a potential V due to a charge q –Using potential energy by charge q and a test charge q 0 

Electric Potential Suppose charge q 0 is moved from pt A to pt B through a region of space described by electric field E. Since there will be a force on the charge due to E, a certain amount of work W AB will have to be done to accomplish this task. We define the electric potential difference as: The potential difference is meaningful Because only potential energy difference is meaningful U=V=0 can be chosen arbitrarily (like for gravity) A B q 0 E

Lecture 4, ACT 1 A single charge ( Q = -1  C) is fixed at the origin. Define point A at x = + 5m and point B at x = +2m. –What is the sign of the potential difference between A and B? (V AB  V B - V A ) (a) V AB <  (b) V AB =  (c) V AB >  x -1  C   A B The simplest way to get the sign of the potential difference is to imagine placing a positive charge at point A and determining whether positive or negative work would be done in moving the charge to point B. A positive charge at A would be attracted to the -1  C charge; therefore NEGATIVE work would be done to move the charge from A to B. E

Electric Potential Define the electric potential of a point in space as the potential difference between that point and a reference point. a good reference point is infinity... we typically set V  = 0 the electric potential is then defined as: for a point charge, the formula is:

Potential from N charges The potential from a collection of N charges is just the algebraic sum of the potential due to each charge separately. x r1r1 r2r2 r3r3 q1q1 q3q3 q2q2 

Electric Dipole z a a  +q -q r r 1 r 2 The potential is much easier to calculate than the field since it is an algebraic sum of 2 scalar terms. Rewrite this for special case r>>a:  Can we use this potential somehow to calculate the E field of a dipole? (remember how messy the direct calculation was?)  r 2 -r 1

E from V? We can obtain the electric field E from the potential V by inverting our previous relation between E and V: Consider 2 plates and a charge q force on q Work done on q F But work-energy theorem Conservative force

E from V? We can obtain the electric field E from the potential V by inverting our previous relation between E and V: We have F So that Therefore

Equipotentials GENERAL PROPERTY: –The Electric Field is always perpendicular to an Equipotential Surface. Why?? Dipole Equipotentials Defined as: The locus of points with the same potential. Example: for a point charge, the equipotentials are spheres centered on the charge. The gradient (  ) says E is in the direction of max rate of change. Along the surface, there is NO change in V (it’s an equipotential!) So, there is NO E component along the surface either… E must therefore be normal to surface

Claim The surface of a conductor is always an equipotential surface (in fact, the entire conductor is an equipotential) Why?? If surface were not equipotential, there would be an Electric Field component parallel to the surface and the charges would move!! Note Positive charges move from regions of higher potential to lower potential (move from high potential energy to lower PE). Equilibrium means charges rearrange so potentials equal. Conductors

Charge on Conductors? How is charge distributed on the surface of a conductor? –KEY: Must produce E=0 inside the conductor and E normal to the surface. Spherical example (with little off-center charge): E=0 inside conducting shell charge density induced on inner surface non-uniform charge density induced on outer surface uniform E outside has spherical symmetry centered on spherical conducting shell. +q

A Point Charge Near Conducting Plane + a q V=0

A Point Charge Near Conducting Plane + - a q The magnitude of the force is The test charge is attracted to a conducting plane Image Charge

Equipotential Example Field lines more closely spaced near end with most curvature. Field lines  to surface near the surface (since surface is equipotential). Equipotentials have similar shape as surface near the surface. Equipotentials will look more circular (spherical) at large r.