Electric Potential and Capacitance Physics Sections 17-1 and 17-2 Electric Potential and Capacitance

Electric Potential Returning to our gravity analogy, lifting an object against gravity requires force, which is applied over a displacement, y. The gravitational potential energy was PEg = Fg•y, where y was the vertical displacement. (Sometimes written h or ∆y.) This is equal to the work done in lifting the object. In a similar way, moving a charge against the E field also requires work. The energy is PEe = Fe•d, where d is the distance moved parallel to the field (opposite to the direction of the field lines for + charge).

Electric Potential Energy = q0 Fe Since, PEe = qEd PEe = Fe•d analog to PEg = mgh gravity electric field + + + + + + + + + + + + + + gravitational field b electric field E y g d Fg – Fe – + q a m – – – – – – – – – – – – – –

Electric Potential PEe Va = q We defined the electric field (E field) as the force per unit charge. Similarly, it is useful to define electric potential as the potential energy per unit charge at a point “a” in the E field. PEe Va = q Electric potential is also known simply as potential. The electric potential, Va, at a single point in the field uses infinity as one reference point, since E equals zero at an infinite distance from the source of the fields.

Electrical Potential Difference The difference in potential between two points, or charged plates, is known as electrical potential difference, potential difference, or voltage. It is the work done by the field per charge in moving the charge from point b to point a. ∆PEe q0Ed ∆V = Ed ∆V = Vb – Va = = q0 q0 This equation is used to find the potential difference between two points a distance d apart in an electric field. Since work done by the field itself equals ∆PEe: Wb→a = q0∆V

Electrical potential near a charge The electrical potential at a point “a” in terms of the charge creating the field, q, is given by: ∞ E∞ = 0 Va = Ed = Er q E = ke Since E is given by: r2 q a Va = ke Ea r q Where r is the distance between point “a” and the charge, q.

Units The unit for electrical potential and for the potential difference between two points in the field can be found by dimensional analysis. PEe ∆V = Since, q0 The units are joules per coulomb. One J/C is defined as one volt, named for Alessandro Volta. 1 J/C = 1 V 1 volt is the potential difference between two infinite parallel plates spaced 1 meter apart and with an E-field equal to 1 N/C.

Water analogy A difference in electrical potential between two points in an electrical field can be thought of as similar to the difference between two points with different water pressure. If two points, A and B, have different water pressures, water fill flow from the point of high pressure to the point of low pressure. In a similar way, electric current will move from a point of high potential to a point of lower potential.

∆V = Ed Wa→b = q∆V ∆V = (2400 N/C) (0.035 m) ∆V = 84 Nm/C = 84 J/C 1. The electric field strength between to large parallel charged plates is 2400 N/C. The plates are 0.035 m apart. What is the potential difference between the plates? ∆V = Ed ∆V = (2400 N/C) (0.035 m) ∆V = 84 Nm/C = 84 J/C = 84 V 2. How much work is done in moving a 5μC charge through a potential difference of 12 V? Wa→b = q∆V W = (5 × 10–6 C) (12 V) = 6 × 10–5 J

Subatomic particles q Va = ke r qe = 1.60 × 10–19 C (3 × 10–6 C) Va = 3. What is the electric potential in volts at a point 5 cm from a charge of 3 × 10–6 C? Va = q r ke (3 × 10–6 C) Va = (9 × 109 Nm2/C2) = 5.4 × 105 V (5 × 10–2 m) = 540 kV Subatomic particles The charge on a single electron is called the elementary unit of charge. qe = 1.60 × 10–19 C Of course for an electron, the sign is negative, and it is an equal value, but positive, for a proton. The electron volt (eV) is an energy unit equal to the energy acquired by an electron as it moves through a potential difference of 1V. 1 eV = 1.6 × 10–19 J

Capacitors, charge storage devices dielectric material A capacitor is a device used to store charge. Capacitors consist of two conductors (plates) separated by an insulator called a dielectric. The Leyden Jar was the first capacitor. It has two sheets of metal foil separated by glass. Modern capacitors can be very small. The plates are metal film. Dielectrics include plastic film, mica, paper, etc.

Capacitance q C = ∆V Units: 1 C 1 F = 1 V Capacitance is the ability of a capacitor to hold electric charge. It is the amount of charge in coulombs per volt of potential difference. q C = ∆V if the charges on the plates are +q and –q, and the potential difference between the plates is ∆V. Units: The unit of capacitance is the farad (F). 1 C Common capacitance units 1 F = 1 V 1 mF = 0.001 F 1000 mF = 1 F 1 μF = 10–6 F 106 μF = 1 F or uF, MFD 1 pF = 10–12 F 1012 pF = 1 F “pico”

Types of capacitors mica glass ceramic tantalum type dielectric range max V leakage stability mica 1pF-0.01μF 100-600V low glass 10pF-1000pF low good ceramic 10pF-1μF 50-30000V moderate poor polypropylene (PP) film polypropylene 100pF-50μF 100-800V PTFE (Teflon) polytetrafluoro-ethylene 1000pF-2μF 50-200V lowest,best best polyester (PET) film (Mylar) polyethylene terephthalate 1000pF-50μF 50-600V tantalum tantalum pentoxide 0.1μF-1000μF 6-100V varies electrolytic aluminum oxide 0.1μF-2.7F 3-600V very high very poor double layer supercapacitor Helmholtz double-layer 0.1F-1000+ 1.5-6V

electrolytic double-layer silver mica polyester tantalum ceramic both 68 and 220 μF double-layer 10 F silver mica 220 and 820 pF polyester 470 pF tantalum both 10 μF ceramic polypropylene blue: 0.002 μF tan: 0.01 μF 0.1 μF surface mount solder mount