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Phys 133 – Chapter 291 Chapter 29 Electric Potential and Field

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Phys 133 – Chapter 292 Overview Force, field, energy, potential

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Phys 133 – Chapter 293 Force, field, energy, potential or

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Fields and potentials Phys 133 – Chapter 294 1. a) E = 0 V/m in throughout some region of space, can you conclude that the potential V = 0 in this region? b) V = 0 V throughout some region of space. Can you conclude that the electric field E = 0 V/m in this region?

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Phys 133 – Chapter 295 Graphically convert between E and V 2. The top graph shows E x vs. x for an electric field parallel to the x-axis. a) Draw the graph of V vs. x in this region of space. Let V = 0 at x = 0m. Add an appropriate scale on the vertical axis. (Hint: integration is the area under the curve) b) Draw a contour map above the x-axis on a diagram like the one below- right and label your equipotential lines every 20 V. 0V has been drawn already. C) Draw several electric field vectors on top of the contour map. 24 20 40 E x (V/m) 12034 x(m) 0 V

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Phys 133 – Chapter 296 --Find the electric potential everywhere for a sphere (radius R) with charge (Q) uniformly distributed. Take V=0 at infinity. --Sketch V vs r and E r vs r. From Chap 27 E field is: Problem: Potential of sphere

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Phys 133 -- Chapter 307 Problem: Potential of sphere (ans) r definition For all r For R < r VrVr V∞V∞ ∆V Finding V r For r < R VrVr VrVr V R ∆V

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Phys 133 – Chapter 298 Find the electric potential everywhere for a sphere (radius R) with charge (Q) uniformly distributed. Problem: Potential of sphere (ans)

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Phys 133 – Chapter 299 Find the x,y and z components of the electric field, given that the electric potential of a disk is given by Problem: Field from Potential

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Phys 133 – Chapter 2910 Find the z component of the electric field, given that the electric potential of a disk is given by Problem: Field from Potential (Answer)

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Phys 133 – Chapter 2911 is perp to equipotential surfaces points downhill (decreasing V) --strength proportional to spacing equipotentials Geometry of potential/field

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Phys 133 – Chapter 2912 Kirchhoff’s loop rule (Conservation of energy)

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Phys 133 – Chapter 2913 --field is zero inside conductor --field is perpendicular at surface --conductor is at equipotential (no work to move) Conductor in equilibrium: field and potential

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Phys 133 – Chapter 2914 --equipotentials are parallel to nearby conductor Conductor in equilibrium: equipotentials

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Phys 133 – Chapter 2915 Do Workbook 30.4, 6, 11, & 12a

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Phys 133 – Chapter 2916 --Find the electric potential everywhere for a point charge (q) at the center of a hollow metal sphere (inner radius a, outer radius b) with charge Q. (Take V=0 at infinity.) --Sketch V vs r and E r vs r. Problem: Finding Potential

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Phys 133 -- Chapter 3017 Problem: Finding Potential (ans) r VrVr V∞V∞ ∆V VrVr V a ∆V For all r For b < r Finding V r For a < r < b For r < a

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Phys 133 -- Chapter 3018 not origin Problem: finding Potential (Answer)

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Phys 133 -- Chapter 3019 -charge separation -not sustained Sources of potential: Capacitor

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Phys 133 -- Chapter 3020 --sustained -- Sources of potential: Battery

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Phys 133 -- Chapter 3021 Capacitors charge separation on capacitor Apply to capacitor

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Phys 133 -- Chapter 3022 --generic circuit elements --imagine battery connection parallel series Circuit geometry

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Phys 133 -- Chapter 3023 Capacitors: series equivalent

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Phys 133 -- Chapter 3024 Capacitors: parallel equivalent

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Phys 133 -- Chapter 3025 seriesparallel VV V 1 + V 2 = V eq V1=V2V1=V2 QQ 1 =Q 2 Q 1 +Q 2 = Q eq Capacitors

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Phys 133 -- Chapter 3026 Do Workbook 30.26 & 27

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Phys 133 -- Chapter 3027 --work done charge separation --or in electric field Energy in capacitor

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Phys 133 -- Chapter 3028 --Find the charge on (Q) and potential difference ( V) across each capacitor. --What is the total energy stored in the system? Problem

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Phys 133 -- Chapter 3029 Problem (ans)

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Phys 133 -- Chapter 3030 Problem (ans)

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Dielectrics change the potential difference The potential between to parallel plates of a capacitor changes when the material between the plates changes. It does not matter if the plates are rolled into a tube as they are in Figure 24.13 or if they are flat as shown in Figure 24.14.

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Table 24.1—Dielectric constants

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Field lines as dielectrics change Moving from part (a) to part (b) of Figure 24.15 shows the change induced by the dielectric. In dielectric In vacuum, energy density is

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Examples to consider, capacitors with and without dielectrics If capacitor is disconnected from circuit, inserting a dielectric changes decreases electric field, potential and increases capacitance, but the amount of charge on the capacitor is unchanged. If the capacitor is hooked up to a power supply with constant voltage, the voltage must remain the same, but capacitance and charge increase

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You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the charges on the plates remain constant. What effect does adding the dielectric have on the potential difference between the capacitor plates? A. The potential difference increases. B. The potential difference remains the same. C. The potential difference decreases. D. not enough information given to decide Q24.8

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You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the charges on the plates remain constant. What effect does adding the dielectric have on the potential difference between the capacitor plates? A. The potential difference increases. B. The potential difference remains the same. C. The potential difference decreases. D. not enough information given to decide A24.8

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You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the charges on the plates remain constant. What effect does adding the dielectric have on the energy stored in the capacitor? A. The stored energy increases. B. The stored energy remains the same. C. The stored energy decreases. D. not enough information given to decide Q24.9

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You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the charges on the plates remain constant. What effect does adding the dielectric have on the energy stored in the capacitor? A. The stored energy increases. B. The stored energy remains the same. C. The stored energy decreases. D. not enough information given to decide A24.9

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You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the potential difference between the plates remains constant. What effect does adding the dielectric have on the amount of charge on each of the capacitor plates? A. The amount of charge increases. B. The amount of charge remains the same. C. The amount of charge decreases. D. not enough information given to decide Q24.10

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You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the potential difference between the plates remains constant. What effect does adding the dielectric have on the amount of charge on each of the capacitor plates? A. The amount of charge increases. B. The amount of charge remains the same. C. The amount of charge decreases. D. not enough information given to decide A24.10

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You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the potential difference between the plates remains constant. What effect does adding the dielectric have on the energy stored in the capacitor? A. The stored energy increases. B. The stored energy remains the same. C. The stored energy decreases. D. not enough information given to decide Q24.11

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You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the potential difference between the plates remains constant. What effect does adding the dielectric have on the energy stored in the capacitor? A. The stored energy increases. B. The stored energy remains the same. C. The stored energy decreases. D. not enough information given to decide A24.11

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