Electrical Energy and Capacitance Chapter 18 Electrical Energy and Capacitance (But we don’t have to cover capacitance)

18.1 Electrical Potential Energy Objectives 1. Define electrical potential energy 2. Compare the electrical potential energy for various charge distributions (these charges distributions are uniform and non-uniform electric fields)

A Look Back at Gravitational Potential Energy PEgrav = mgh PEgrav=mgh h PEgrav=0

Electric Potential Energy Potential associated with a charge due to its position relative to a source of electric force Non-uniform E-field Uniform E-field

Consider: Uniform Electric Field

Charge Movement in E Field vs PEelectric If the charge is moving…. + Charge - Charge With E Loses PEelectric Gains PE electric Opposite E Gains PEelectric

Electrical Potential Energy (in a uniform field) ΔPEelectric = -qE(Δd) q = charge (C) E = electric field strength (N/C) Δd = displacement (m) from the reference point in the direction of the field If we assume PEi=0 at di=0, then this equation can also be written as PEe = -qEd

PEe for Uniform E-field A charge of 7.5μC moves a distance of 0.25m through a uniform electric field with magnitude 5.50x106 V/m. How much did the charge’s potential energy change in that distance? ANS: 10.3J An electron moves a distance of 0.035m through a uniform electric field between two oppositely charged parallel plates. In that span, the electron’s potential energy changed by 5.60x10-15J. What is the magnitude of the E-field, and what direction did the electron move (toward the + plate or – plate)? ANS: 9.99x105 V/m, moved toward - plate

Electrical Potential Energy Associated with a Point Charge   …because point charges produce non-uniform electric fields

Regarding PEelectric for point charges… The reference point for electrical potential energy is assumed to be at infinity. Note that PEelec goes to zero as r goes to infinity. Because like charges repel, positive work must be done to bring them together. So, PEelec is positive for like charges and negative for unlike charges. For determining PEelec for more than two charges, calculate PEelec for each pair then add the energies.

PEe for Non-Uniform E-field In one model of the hydrogen atom, an electron in its lowest energy state moves in a circular orbit about the nucleus (a single proton) at a distance of 5.29x10-11m. Find the electrical potential energy of the hydrogen atom. Answer: PEe = -4.35x10-18 J

PEe for More than Two Point Charges A point charge of 3.0nC is located at the origin. Another charge of 6.0nC is located at (0.0, 30.0)cm. What is the electrical potential energy of the system if a third charge of 4.0nC is at (0.0, 60.0)cm? b) What is the third charge is at (0.0, -60.0)cm? c) What is the third charge is -6.0nC and is located at (0.0, -60.0)cm? ANS: a) 1.44x10-6J b) 9.6x10-7J c) -8.99x10-8J

18.2 Potential Difference Objectives Distinguish between electrical potential energy, electric potential, and potential difference. Compute the potential difference for for various charge distributions (i.e., uniform and non-uniform electric fields).

Electric Potential (V) …is the electrical potential energy associated with a charged particle divided by the charge of the particle    

Potential Difference (ΔV) …is the change in electrical potential energy associated with a charged particle divided by the charge of the particle.    

What’s another name for PE? Hint:What do we have to do to a charged particle if we want to increase it’s PEelec? PE aka “Work” (W)   units for PE and for work = joules (J)

More About Potential Difference Potential difference is often referred to as “voltage”. As a 1C charge moved through a potential difference of 1V, the charge gains (or loses) 1J of energy. Common potential differences (voltages) are 12V for a car battery and 120V between the two slots in a household electrical outlet.

Potential Difference in a Uniform Electric Field   We know V = And ΔPEelectric = -qEΔd (uniform field)   So ΔV = -EΔd (where Δd is displacement from a reference point in the direction of the electric field)

...therefore E units must be ?? V = -E d Notice…..new units for E !! V units is volts (V) d is in meters (m) ...therefore E units must be ??  

ΔV for uniform electric field A proton is released from rest in a uniform E-field with a magnitude of 8.0x104 V/m. The proton moves 0.50 m as a result. Find: a) The potential difference between the initial and final positions of the proton. b) The change in electrical potential energy of the proton as a result of this displacement. ANS: a) -4.0x104 V b) -6.4x10-15 J

Potential Difference at Some Location Near a Point Charge         (compares the potential difference between a point at infinity and some location near a point charge)

ΔV near a point charge Find the potential difference between a point infinitely far away from and a point 1.0 cm from a proton. ANS: 1.44x10-7 V

Conservation of Energy When we think about individual charges moving through uniform or non-uniform electric fields, we’re going to assume that the total energy of the charge remains constant (i.e., energy is conserved). So, we can say….. MEi = MEf KEi + PEgi + PEsi + PEei= KEf + PEgf + PEsf + PEef But in our electrical calculations we typically are only dealing with PEe, so… KEi + PEei = KEf + PEef

Conservation of ME A proton is accelerated from rest through a potential difference of 220V. What is the velocity of the proton at this point? ANS: 2.05x105 m/s

Water Analogy

PEelectric, Electric Potential, and Potential Difference in a Battery The potential difference between the positive and negative terminals is 9V, where the electric potential at the negative terminal is 0V, and the electric potential at the positive terminal is 9V. When hooked to an electrical device, the charge moves inside the battery from negative to positive terminal. The battery does work on the charge in order to move it from the (-) to the (+) terminal, so PEelectric increases.

More on PEelectric, Electric Potential and Potential Difference