Ch 29 The Electric Potential 講者： 許永昌 老師

Contents The Electric Potential Energy (電位能) Of a point charge in a uniform Electric Field Of two point charges Of many point charges Of a dipole The Electric Potential (電位) Inside a parallel-plate capacitor Of a point charge Of many charges

Review of Mechanical energies (請預讀P881~P882) Conservative force  Win =-DU  Potential Energy. Draw the interaction diagram. W= System. DEmech=DK+DU=Wext. Draw the before-and-after pictorial representation. Draw the energy diagram. dr F before after + + + + -v v

Compare with Gravitational force Coulomb force Two particles M and Q M  0 QR Conservative force? Yes Potential Energy of two particles Field Potential of a particle with source of uniform field DU=mgDy

Exercise Whether the change of potential is positive, negative, or zero? This particle is (a) proton (b) electron (c)hydrogen atom. The elements of a system? i f f i + - - i + - f Hint: Win=qEdr=-DU ------ ++++++ ------ ++++++ f f f i E i i

A uniform Field (請預讀P883~P884) Interaction diagram: Since the charges on the parallel plates are fixed, their contribution for the net potential energy will be zero. ------ ++++++ + + Positive charged plate Negative charged plate -

The Potential Energy of Point Charges (請預讀P885~P887) Force pair  Potential (conservative force) 1 2 Two concepts: Force pair: Coulomb force is a conservative force: v1 v2 v2-v1 fixed Stop to Think: 為何此處寫U而非DU?試著寫出積分式。 Hint: 與哪裡當作zero of potential energy 有關。

Potential energy of Multiple Point Charges Because each coulomb force pair is related to one potential energy, the sum of potential energy can be written as

The Potential Energy of a Dipole (請預讀P889) Model: Assume that the dipole is small enough so that the electric field is uniform for this dipole. Derivation:

Homework Student Workbook 1, 5, 6, 8

The electric Potential (請預讀P890~P892) Question: When we say two charged particles have a potential energy, an energy that can be converted to a tangible (明確的) kinetic energy of motion, where is the energy? In analogy with the electric field, people define electric potential as Unit: 1 volt =1 V =1 J/C. Both E and V are the properties of the source charges.

What good is the electric potential? Answers: V is the ability of the source charges to have an interaction if a charge q shows up. This potential is present throughout space regardless of whether or not charge q is there to experience it. The interaction energy of any charge q in that region of space with the source charges is U=qV. The Electric Potential V V is a property of the source charges which is related to the electric field. The Electric Potential Energy U U is the interaction energy of a charged particle with the source charges.

Exercises Which are the sources? Rank in order the electric potentials at the numbered points. 1 2 2 1 + - - 1 + - 2 Hint: Win=qEdr=-DU ------ ++++++ ------ ++++++ 2 2 2 1 E 1 1

The electric potential inside a parallel-plate capacitor (請預讀P893~P896) Strategy: E(U)V. Graphical representations: We can choose different points as V=0 because the important one is DV.

Potential and Potential difference Sometimes you saw people wrote Ohm’s law as V=IR and the capacitor equation as Q=CV, however, V here were related to the potential difference in fact. Therefore, Ohm’s Law: DV=IR. Capacitor Equation: Q=CDV. The potential difference between two plates. A battery is a source of potential usually. I R, DV

Homework Student Workbook 9, 12, 15

The Electric Potential of a Point Charge (請預讀P897~P898) V of a source charge q can be gotten from the potential energy of q and q’ where q’ is located at the position we want to get the electric potential. q r q’ q

Exercise For the situation shown in the figure, find The potential at points a and b. The potential difference between a and b. The speed at point b of a proton that was moving to the right at point a with a speed of 4.0105 m/s. How about the speed at point c? c 1 cm a b 10nC + 1 cm 3 cm

The Electric Potential of Many and continuous distribution of charges (請預讀P899~P902) Code:dipole.m Basic Concept: It obeys the principle of superposition; however, it is easier than the calculation of electric field because the potential is scalar.

Homework Student Workbook Student Textbook 17, 21, 22, 26, 27 請自行製作 Terms and Notation的卡片。