Chapter 18 Electrical Energy and Capacitance

18.1 Electrical Potential Energy Objectives 1. Define electrical potential energy 2. Compare the electrical potential energy for various charge distributions

A Look Back at Gravitational Potential Energy PE grav =mgh h PE grav =mgh PE grav =0

Electric Potential Energy Potential associated with an object due to its position relative to a source of electric force

Consider: Uniform Electric Field

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

Electrical Potential Energy PE electric = -qEd q = charge (C) E = electric field strength (N/C) d = displacement (m) from the reference point in the direction of the field (in a uniform field)

Electrical Potential Energy for a Pair of Charges PE electric = k C q 1 q 2 r …because point charges produce non-uniform electric fields

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

Problem: 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 5.29x m. Find the electrical potential energy of the hydrogen atom. Which equation for PE electric ? PE electric = k C q 1 q 2 r Answer: PE electric = -4.35x J

18.2 Potential Difference Objectives 1.Distinguish between electrical potential energy, electric potential, and potential difference. 2.Compute the potential difference for for various charge distributions.

Water Analogy

Electric Potential V = PE electric q …is the electrical potential energy associated with a charged particle divided by the charge of the particle

Potential Difference …is the change in electrical potential energy associated with a charged particle divided by the charge of the particle. V =PE electric q units = J/C = volts (V)

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

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. More About Potential Difference

Potential Difference in a Uniform Electric Field And PE electric = -qEd (uniform field) V =We know PE electric q SoV = -qEd q dV = -E (where d is displacement from a reference point in the direction of the electric field)

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

Potential Difference at Some Location Near a Point Charge PE electric q We know And PE electric = k C q 1 q 2 (for point charges) r V = k C q 1 q 2 q 1 r So V = k C q r V = (compares the potential difference between a point at infinity and some location near a point charge)

Questions 1. Find the potential difference between a point infinitely far away from and a point 1.0 cm from a proton. 2. A proton is released from rest in a uniform E- field with a magnitude of 8.0x10 4 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.

Answers x V 2.a) -4.0 x 10 4 V b) -6.4 x J

PE electric, 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 PE electric increases.

More on PE electric, Electric Potential and Potential Difference

18.3 Capacitance Objectives 1.Relate capacitance to the storage of electrical potential energy in the form of separated charges 2.Calculate the capacitance of various devices 3.Calculate the energy stored in a capacitor

Capacitance …is the ability of a conductor to store energy in the form of electrically separated charges

Parallel-plate Capacitor Parallel conductive plates in a circuit with a charge source (V). Close the switch and the charge flows until the voltage across the plates equals the applied voltage. Charge flows from one plate to the other, leaving behind a plate that is equally (but oppositely) charged. Open the switch and charge (and electrical potential energy) are stored.

Capacitance – Basic Equation C = Q V capacitance = magnitude of charge on each plate potential difference C = farads (F) = C/V

Capacitance and PE electric PE electric = ½ QV and since C = Q V substituting gives us: PE electric = ½ CV2V2 and PE electric = Q 2 2C

Questions 1. A parallel-plate capacitor has a charge of 6.0x10 -6 C when charged by a potential difference of 1.25V. a) Find its capacitance b) How much potential energy is stored when this capacitor is connected to a 1.5V battery? Answers:a)4.8x10 -6 F b)5.4x10 -6 J