Presentation on theme: "Chapter 30. Potential and Field"— Presentation transcript:
1 Chapter 30. Potential and Field To understand the production of electricity by solar cells or batteries, we must first address the connection between electric potential and electric field.Chapter Goal: To understand how the electric potential is connected to the electric field.
2 Chapter 30. Potential and Field Topics:Connecting Potential and FieldSources of Electric PotentialFinding the Electric Field from the PotentialA Conductor in Electrostatic EquilibriumCapacitance and CapacitorsThe Energy Stored in a CapacitorDielectrics
3 Stop to think page 916Stop to think page 918Stop to think page 920Stop to think page 922Stop to think page 927
6 Finding the Potential from the Electric Field The potential difference between two points in space iswhere s is the position along a line from point i to point f. That is, we can find the potential difference between two points if we know the electric field.We can think of an integral as an area under a curve. Thus a graphical interpretation of the equation above is
14 Batteries and emfThe potential difference between the terminals of an ideal battery isε-emf (electromotive force)In other words, a battery constructed to have an emf of 1.5V creates a 1.5 V potential difference between its positive and negative terminals.The total potential difference of batteries in series is simplythe sum of their individual terminal voltages:
15 Finding the Electric Field from the Potential In terms of the potential, the component of the electric field in the s-direction isNow we have reversed Equation 30.3 and have a way to find the electric field from the potential.
17 EXAMPLE 30.4 Finding E from the slope of V QUESTION:
18 Kirchhoff’s Loop LawFor any path that starts and ends at the same pointStated in words, the sum of all the potential differences encountered while moving around a loop or closed path is zero.This statement is known as Kirchhoff’s loop law.
20 Capacitance and Capacitors The ratio of the charge Q to the potential difference ΔVC is called the capacitance C:Capacitance is a purely geometric property of two electrodes because it depends only on their surface area and spacing. The SI unit of capacitance is the farad:1 farad = 1 F = 1 C/V.The charge on the capacitor plates is directly proportional to the potential difference between the plates.
22 Combinations of Capacitors If capacitors C1, C2, C3, … are in parallel, their equivalent capacitance isIf capacitors C1, C2, C3, … are in series, their equivalent capacitance is
23 The Energy Stored in a Capacitor Capacitors are important elements in electric circuits because of their ability to store energy.The charge on the two plates is ±q and this charge separation establishes a potential difference ΔV = q/C between the two electrodes.In terms of the capacitor’s potential difference, the potential energy stored in a capacitor is
24 EXAMPLE 30.9 Storing energy in a capacitor QUESTIONS:
25 The Energy in the Electric Field The energy density of an electric field, such as the one inside a capacitor, isThe energy density has units J/m3.
27 DielectricsThe dielectric constant, like density or specific heat, is a property of a material.Easily polarized materials have larger dielectric constants than materials not easily polarized.Vacuum has κ = 1 exactly.Filling a capacitor with a dielectric increases the capacitance by a factor equal to the dielectric constant.