Presentation on theme: "Chapter 30. Potential and Field"— Presentation transcript:
1Chapter 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.
2Chapter 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
3Stop to think page 916Stop to think page 918Stop to think page 920Stop to think page 922Stop to think page 927
6Finding 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
14Batteries 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:
15Finding 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.
17EXAMPLE 30.4 Finding E from the slope of V QUESTION:
18Kirchhoff’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.
20Capacitance 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.
22Combinations 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
23The 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
24EXAMPLE 30.9 Storing energy in a capacitor QUESTIONS:
25The 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.
27DielectricsThe 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.