Chapter 14, MHR-Fields and Forces Chapter 17 Giancoli Electrical Potential

Today’s Topics Electric Potential Energy Electric Potential Electric Equi-potential Lines

Work You do work when you push an object up a hill The longer the hill the more work you do: more distance The steeper the hill the more work you do: more force The work W done on an object by an agent exerting a constant force is the product of the component of the force in the direction of the displacement and the magnitude of the displacement

Work done by gravity m mg d

Energy is capacity to do work note E p aka U G Gravitational Potential Energy Kinetic Energy Energy can be converted into other forms of energy When we do work on any object we transfer energy to it Energy cannot be created or destroyed

A person lifts a heavy box of mass ‘m’ a vertical distance ‘h’ They then move a distance ‘d’, carrying the box How much work is done carrying the box? Quiz

Conversion of Gravitational Potential Energy to Kinetic Energy m mg m v Work done on object h

What’s an electric field? A region around a charged object through which another charge will experience a force Convention: electric field lines are drawn out of (+) and into (-); so the lines will show the movement of a “positive test charge” E = F / q units are in N/C +Q

Electric Potential Energy charges also have electrical potential energy +Q d v

Electric Potential Energy Work done (by electric field) on charged particle is QEd Particle has gained Kinetic Energy (QEd) Particle must therefore have lost Potential Energy  U=-QEd

Electric Potential The electric potential energy depends on the charge present We can define the electric potential V which does not depend on charge by using a “test” charge Change in potential is change in potential energy for a test charge per unit charge for uniform field

Electric Potential compare with the Electric Field and Coulomb Force If we know the potential field this allows us to calculate changes in potential energy for any charge introduced

Electric Potential Electric Potential is a scalar field it is defined everywhere but it does not have any direction it doesn’t depend on a charge being there

Electric Potential, units SI Units of Electric Potential Units are J/C Alternatively called Volts (V) We have seen Thus E also has units of V/m

Potential in Uniform field +Q AB C d ||

Electric Potential of a single charge + E B A Advanced

Equi-potential Lines Like elevation, potential can be displayed as contours A contour diagram Like elevation, potential requires a zero point, potential V=0 at r=  Like slope & elevation we can obtain the Electric Field from the potential field

Potential Energy in 3 charges Q2Q1Q3

Capacitors A system of two conductors, each carrying equal charge is known as a capacitor

- Capacitance of charged sphere +Q r=  definition R potential due to isolated charge

Capacitors - + +Q-Q e.g. 1: two metal spheres e.g. 2: two parallel sheets Each conductor is called a plate

Capacitance Capacitance…….. is a measure of the amount of charge a capacitor can store (its “capacity”) Experiments show that the charge in a capacitor is proportional to the electric potential difference (voltage) between the plates.

Units Thus SI units of capacitance are: C/V This unit is also known as the farad after Michael Faraday Remember that V is also J/C so unit is also C 2 J -1 1F=1C/V

Capacitance The constant of proportionality C is the capacitance which is a property of the conductor Experiments show that the charge in a capacitor is proportional to the electric potential difference (voltage) between the plates.

Capacitance of parallel plates +Q-Q Intutively The bigger the plates the more surface area over which the capacitor can store charge C  A E Moving plates togeth`er Initially E is constant (no charges moving) thus  V=Ed decreases charges flows from battery to increase  V  C  1/d Never Ready + VV

Batteries, Conductors & Potential Never Ready + A battery maintains a fixed potential difference (voltage) between its terminals A conductor has E=0 within and thus  V=Ed=0 VV  V= 0

Capacitance of parallel plates +Q-Q Physically E Never Ready + property of conductor VV