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There will be a quiz next class period, Feb 1, covering Ch 22 and the beginning of Ch 23 (what we cover in class today) Definitions • Electric potential—Potential energy per unit charge at a point in an electric field • Path integral (line integral)—An integral performed over a path such as the path a charge q follows as it moves from one point to another • Volt—The unit of electric potential. 1V = 1 J/C • Electron volt (eV)—the energy that an electron (or proton) gains or loses by moving through a potential difference of 1 V. • Equipotential surface—A surface consisting of a continuous distribution of points having the same electric potential Electric Potential • Electric force is a conservative force, therefore there is a potential energy associated with it. • We can define a scalar quantity, the electric potential, associated with it. r r r r W Efield FE dl qE dl r r dU qE dl r B r U q E dl A r B r U V A E dl q Electric Potential Energy Concepts of work, potential energy and conservation of energy For a conservative force, work can always be expressed in terms of potential energy difference b Wa b F d l U (U b U a ) a Energy Theorem For conservative forces in play, total energy of the system is conserved Ka U a Kb U b • The line integral used to calculate V does not depend on the path taken from A to B; therefore pick the most convenient path to integrate over Electric Potential • We can pick a 0 for the electric potential energy U 0r • U is independent of any charge q that can be placed in the Electric field • U has a unique value at every point in the electric field • U depends on a location in the E field only Wa b Fd q0 Ed U q0 Ey Wa b U q0 E ( ya yb ) Potential energy U increases as the test charge q0 moves in the direction opposite to the electric force F q0 E: it decreases as it moves in the same direction as the force acting on the charge Electric Potential Energy of Two Point Charges b Wa b rb qq0 F d l ke 2 cos dl r a r a Wa b 1 1 ke qq0 ra rb qq0 U ke r Electric potential energy of two point charges Example: Conservation of energy with electric forces A positron moves away from an a– particle m p 9.1 1031 kg 0 a-particle positron ma 7000m p qa 2e r0 1010 m V0 3 106 m / s What is the speed at the distance r 2r0 2 1010 m ? What is the speed at infinity? Suppose, we have an electron instead of positron. What kind of motion we would expect? Conservation of energy principle K0 U 0 K1 U1 Electric Potential Energy of the System of Charges Potential energy of a test charge q0 in the presence of other charges U q0 qi 4 0 i r i Potential energy of the system of charges (energy required to assembly them together) U 1 qi q j 4 0 i j r ij Potential energy difference can be equivalently described as a work done by external force required to move charges into the certain geometry (closer or farther apart). External force now is opposite to Wa b (U b U a ) Fext d l the electrostatic force Electric potential is electric potential energy per unit charge Finding potential (a scalar) is often much easier than the field (which is a vector). Afterwards, we can find field from a potential U V q0 Units of potential are Volts [V] 1 Volt=1Joule/Coulomb If an electric charge is moved by the electric field, the work done by the field Wa b U (Va Vb ) q0 q0 Potential difference if often called voltage Two equivalent interpretations of voltage: 1.Vab is the potential of a with respect to b, equals the work done by the electric force when a UNIT charge moves from a to b. 2. Vab is the potential of a with respect to b, equals the work that must be done to move a UNIT charge slowly from b to a against the electric force. Potential due to the point charges 1 dq V 4 0 r Potential due to a continuous distribution of charge Finding Electric Potential through Electric Field b Wa b Va Vb E d l q0 a Some Useful Electric Potentials • For a uniform electric field r r r V E dl E • For a point charge q V ke r • For a series of point charges qi V ke ri r r r dl E l Potential of a point charge Moving along the E-field lines means moving in the direction of decreasing V. As a charge is moved by the field, it loses it potential energy, whereas if the chargeis moved by the external forces against the E-field, it acquires potential energy • Negative charges are a potential minimum • Positive charges are a potential maximum Positive Electric Charge Facts • For a positive source charge – Electric field points away from a positive source charge – Electric potential is a maximum – A positive object charge gains potential energy as it moves toward the source – A negative object charge loses potential energy as it moves toward the source Negative Electric Charge Facts • For a negative source charge – Electric field points toward a negative source charge – Electric potential is a minimum – A positive object charge loses potential energy as it moves toward the source – A negative object charge gains potential energy as it moves toward the source