Phy 203: General Physics III Ch 19: Electric Potential Energy & the Electric Potential Lecture Notes

Electric Potential Energy When charge is in an electric field, the electric force exerted upon it, as it moves from one point (A) to another point (B) can do work: W AB =F E.  s. cos  This only works when the applied force (F E ) is constant! When FE is not constant, the work performed is equal to the difference in electric potential energy (EPE): W AB =EPE A -EPE B Note: EPE is similar to gravitational PE (PE grav ) –it is the energy associated to the position of an object subject to an electric force –units are joules (J)

Electric Potential the electric potential (V) is the electric potential energy per unit charge: V=EPE/q –in this manner, V associated with a position can be expressed without concern for the specific charge present –the SI units are joules/coulomb (J/C), called the volt (V) the work performed on an electric charge is related to the change in electric potential (  V) and its charge (q): -W AB =q.  V or  V = -W AB /q Since F E =qE and W AB = F E.  s we can combine them to obtain: E = -  V/  s

Alessandro Volta ( ) Italian physicist & inventor First person to isolate methane Fascinated with electricity at an early age Pioneered the field of electrochemistry constructed the first battery to produce electricity (called a voltaic pile)

Electric Potential (for a point charge) The E field for a point charge is The work required to bring a “test” charge (q o ) from “infinity” to a position r is W = EPE r  – EPE  = EPE r {since EPE  = 0} The EPE is related to F E and r: The electric potential (V) at r then becomes:

Capacitors & Dielectrics The electric field (E) within the plates of a capacitor is constant but the electric potential (V) is not The electric potential (V) is higher at the positive charged plate (+q) and lower at the negative charged plate (-q)  V = - E.  s where  s is the plate separation As the capacitor is charged, the charge that builds up at each plate is proportional to the potential difference across the plates Q ~  V The capacitance (C) is defined as as the ratio: C = Q/  V (or Q/V where one of the plates is V o =0V)

Capacitors & Dielectrics For a parallel plate capacitor: C=   o A/d) Where –A is the surface area –d is the plate separation –K is the dielectric constant (E=E o ) Note: For vacuum or air-filled capacitor:  ~1 For other materials:  >1

Energy Stored in a Capacitor It takes work to charge a capacitor, that work is stored as electrical potential energy: The stored energy per unit volume (E/V) for a parallel plate capacitor is: (the Energy Density)