Chapter 29

Phys 133 – Chapter 29 1

Chapter 29

Electric Potential and Field


Overview Force, field, energy, potential


Force, field, energy, potential

or

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?


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.

2 4

20

40

Ex (V/m)

1 20 3 4

x(m)x(m)

0 V


--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:

Problem: Potential of sphere

Phys 133 -- Chapter 30 7

Problem: Potential of sphere (ans)

rdefinition

For all r

For R < r

Vr V∞

∆VFinding Vr

For r < RVr

Vr

VR

∆V


Find the electric potential everywhere for a sphere (radius R) with charge (Q) uniformly distributed.

Problem: Potential of sphere (ans)


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


Find the z component of the electric field, given that the electric potential of a disk is given by

Problem: Field from Potential (Answer)


is perp to equipotential surfaces

points downhill (decreasing V)

--strength proportional to spacing equipotentials

Geometry of potential/field


Kirchhoff’s loop rule(Conservation of energy)


--field is zero inside conductor

--field is perpendicular at surface

--conductor is at equipotential (no work to move)

Conductor in equilibrium: field and potential


--equipotentials are parallel

to nearby conductor

Conductor in equilibrium: equipotentials


Do Workbook 30.4, 6, 11, & 12a


--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.

Problem: Finding Potential


Problem: Finding Potential (ans)

r

Vr V∞

∆V

Vr

Va

∆V

For all r

For b < r

Finding Vr

For a < r < b

For r < a


not origin

Problem: finding Potential (Answer)


-charge separation

-not sustained

Sources of potential: Capacitor


--sustained

--

Sources of potential: Battery


Capacitors charge separation on capacitor

Apply to capacitor


--generic circuit elements

--imagine battery connection

parallel

series

Circuit geometry


Capacitors: series equivalent


Capacitors: parallel equivalent


series parallel

V V1+V2= Veq V1=V2

Q Q1=Q2 Q1+Q2= Qeq

Capacitors


Do Workbook 30.26 & 27


--work done charge separation

--or in electric field

Energy in capacitor


--Find the charge on (Q) and potential difference (V) across each capacitor.

--What is the total energy stored in the system?

Problem


Problem (ans)


Problem (ans)

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.

Table 24.1—Dielectric constants

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

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

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


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.


A24.8


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.


Q24.9







A24.9

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.


Q24.10


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.


A24.10







Q24.11







A24.11

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Chapter 29