# Electric Potential and Field

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Electric Potential and Field
Chapter 29 Electric Potential and Field Phys 133 – Chapter 29

Overview Force, field, energy, potential
Find potential from field: Workbook: 30.2, 5 Phys 133 – Chapter 29

Force, field, energy, potential
Find potential from field: Workbook: 30.2, 5 or Phys 133 – Chapter 29

Fields and potentials 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? Phys 133 – Chapter 29

Graphically convert between E and V 2. The top graph shows Ex vs
Graphically convert between E and V 2. The top graph shows Ex 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. Ex (V/m) 0 V 40 20 1 2 3 4 2 4 x(m) x(m) Phys 133 – Chapter 29

Problem: Potential of sphere
--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 Er vs r. From Chap 27 E field is: Phys 133 – Chapter 29

Problem: Potential of sphere (ans)
Finding Vr ∆V definition VR r Vr Vr V∞ For all r ∆V For R < r For r < R Vr Phys Chapter 30

Problem: Potential of sphere (ans)
Find the electric potential everywhere for a sphere (radius R) with charge (Q) uniformly distributed. Phys 133 – Chapter 29

Problem: Field from Potential
Find the x,y and z components of the electric field, given that the electric potential of a disk is given by Phys 133 – Chapter 29

Find the z component of the electric field, given that the electric potential of a disk is given by Phys 133 – Chapter 29

Geometry of potential/field
 is perp to equipotential surfaces points downhill (decreasing V) --strength proportional to spacing equipotentials Phys 133 – Chapter 29

Kirchhoff’s loop rule (Conservation of energy)
Phys 133 – Chapter 29

Conductor in equilibrium: field and potential
--field is zero inside conductor --field is perpendicular at surface --conductor is at equipotential (no work to move) Phys 133 – Chapter 29

Conductor in equilibrium: equipotentials
--equipotentials are parallel to nearby conductor Phys 133 – Chapter 29

Do Workbook 30.4, 6, 11, & 12a Phys 133 – Chapter 29

Problem: Finding Potential
--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 Er vs r. Phys 133 – Chapter 29

Problem: Finding Potential (ans)
Finding Vr ∆V For all r Va r Vr Vr V∞ For b < r For r < a ∆V For a < r < b Phys Chapter 30

not origin Phys Chapter 30

Sources of potential: Capacitor
-charge separation -not sustained Phys Chapter 30

Sources of potential: Battery
--sustained -- Phys Chapter 30

Capacitors Apply to capacitor charge separation on capacitor
Phys Chapter 30

Circuit geometry --generic circuit elements
--imagine battery connection parallel series Phys Chapter 30

Capacitors: series equivalent
Phys Chapter 30

Capacitors: parallel equivalent
Phys Chapter 30

Capacitors series parallel V V1+V2= Veq V1=V2 Q Q1=Q2 Q1+Q2= Qeq
Phys Chapter 30

Do Workbook & 27 Phys Chapter 30

Energy in capacitor --work done charge separation
--or in electric field Phys Chapter 30

Problem --Find the charge on (Q) and potential difference (V) across each capacitor. --What is the total energy stored in the system? Phys Chapter 30

Problem (ans) Phys Chapter 30

Problem (ans) Phys Chapter 30

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 or if they are flat as shown in Figure

Table 24.1—Dielectric constants

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

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

Q24.8 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 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

Q24.9 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 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

Q24.10 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 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

Q24.11 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 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

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