Chapter 22 Electric c

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Chapter 22 Electric charge

22-1 Electromagnetism

The early Greek philosophers knew that if you rubbed a piece of amber, it would attract bits of straw. The Greeks also recorded the observation that some naturally occurring “stones” would attract iron.

The sciences of electricity and magnetism developed separately for centuries – until 1820 when Oersted found an electric current in a wire can deflect a magnetic compass needle.

The new science of electromagnetism (the combination of electrical and magnetic phenomena) was developed further by research workers in many countries – Michael Faraday and later James Clerk Maxwell.

22-2 Electric charge

An intrinsic characteristic of the fundamental particles making up those objects.

Two kinds: positive and negative

Electrical isolation: for example, a charged rod is suspended from a thread so that its charge cannot change.

Charges with the same electrical sign repel each other, and charges with opposite electrical signs attract each other.

22-3

Conductors: some of the negative charge can move rather freely.

Insulators (nonconductors): none of the charge can move freely.

Ground: setting up a pathway of conductors between an object and Earth’s surface.

Discharge: neutralizing the object by eliminating an unbalanced positive or negative charge.

Electrons: negatively charged Protons: positively charged Neutrons: electrically neutral

In atoms, for example copper, some of their outermost electrons do not remain attached to the individual atoms but become free to more within the solid. These mobile electrons are called conduction electrons.

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Demonstration of the mobility of charge in a

conductor.

Induced charge: some of its positive and negative charges have been separated.

Semiconductors are materials that are intermediate between conductors and insulators.

Superconductors: no resistance to the movement of charge.

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The Si unit of charge is the coulomb: one coulomb is the amount of charge that is transferred through the cross section of a wire in 1 second when there is a current of 1 ampere in the wire.

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If excess charge is placed on a spherical shell that is made of conducting material, the excess charge spreads uniformly over the (external) surface.

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Six fixed charged particles where a=2.0cm and Θ=30^ο.All six particles have the same magnitude of charge, q=3.0*10^-6C. What is the net electrostatic force F, acting on q, due to the other charges?

vfd

a a Θ

2a a a

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F¹² = F¹⁴ = ^{1 2}₂

0 (2 ) 4

1 a

q q

πε

F¹³ = F¹⁵ = F¹⁶ = ¹ ₂³ 4 0

1 a

q q

πε

F¹ = F¹⁶ - 2F¹³

sin θ

= ¹ ₂⁶

4 0

1 a

q q

πε ^- θ

πε ^sin

4 2

2 3 1

0 a

q

q

q¹ = q³ and θ = 30°

F¹ =0

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Quarks, the constituent particles of protons and neutrons, have charges of ±e/3 or ±2e/3, but they apparently cannot be detected individually. For this and for historical reasons, We do not take their charges to be the elementary charge.

An electrically neutral penny, of mass m=3.11g, contains equal amounts of positive and negative charge.

(a) Assuming that the penny is made entirely of copper, what is the magnitude q of the total positive (or negative) charge in the coin?

(b) Suppose that the positive charge and the negative charge in a penny could be concentrated into two separate bundles, loom apart. What attractive force would act on each bundle?

Sol:

(a) Z = 29 N = N_Am/M q = NZe = 137000C

(b) F = ₂² 4 0

1 r q

πε =1.69X10¹⁶(N) large!!

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Exercises:9,20,29,39

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Chater23

Question: If we move q1 toward q2, does the electric field q2, and thus the force acting onq2, change immediately?

Answer: No. Electromagnetic wave at the speed of light C.

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The electric field exists independently of the test charge. (We assume that in our defining procedure, the presence of the test charge does not affect the charge distribution on the charged object.)

Lines of force: electric field lines. A good way to visualize patterns in electric fields.

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Electric field lines extend away from positive charge and toward negative

charge.

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The nucleus of a uranium atom has a radius R of 6.8fm. Assuming that the positive charge of the nucleus is distributed uniformly, determine the electric field at a point on the surface of the nucleus due to that charge.

Sol: Z=92 ₂

4 0

1 R E Ze

= πε =2.9X10²¹(N/C)

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(Can never find q and d separately !)

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Tactics: 1. the element ds, for instance 2. dq=λds

3. d

4. Symmetry

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A disk has a surface charge density σ of +5.3μC/m² on its upper face. (This is a reasonable value for the surface charge density on the photo sensitive cylinder of a photo copying machine, incidentally.)

(a) What is the electric field at the surface of the disk?

C N X E 3.0 10 /

2

5 0

=

= ε σ

(b) Using the binomial theorem, find an expression for the electric field at a point of the central axis far from the disk.

! ...

2 ) 1 (

! 1 1 ) 1

( + = + +n n− x² +

nx x ⁿ

2 / 1 2 2

2 2 2

2 (1 )

) 1 (

+ −

= +

+ = Z

R

Z Z R

Z R

Z Z

! ....

2 ) 2 1 ( 1 2 1

! 1

2 1 1 )

1

( ₄

4 2

2 2

/ 1 2

2 − − − +

− + +

=

+ ⁻

Z R Z

R Z

R

First order ₂

2

1 2

Z

− R

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2 0 2

2

0 4

)] 1 1 2

1 ( 1

2 [ Z

q Z

E R

πε ε

σ _{− − − =}

=

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Exercises: 19,30,33,51

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Chapter 24

A new formation of coulomb’s law – Gauss’ law

Gaussian surface: a hypothetical closed surface central to Gauss’ law

Description: Gauss’ law relates the electric fields at points on a closed Gaussian surface and the net charge enclosed by that surface.

Φ: The volume flow rate, volume per unit time.

υ: Uniform velocity A: square loop of area

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First thought: repulsionÆ reasonable.

Inside the conductor, EK

must be zero. If this were not so, the field would exert forces on the conduction electrons, causing an electric current.

Important theorem: E=0 inside a conductor.

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(External electric field for conducting surface)

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edge effect of fringing.

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Cf. Gravitation

r-2 , r≥R r , r≤R

Results: E∝

{

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Chapter 25

Electrostatic force is a conservative forceÆ we can assign an electric potential energy U to the system.

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Equipotential surfaces: a surface that all adjacent points have the same electric potential.

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(a) What is the electric potential V at a distance r=2.12x10^-10m from the nucleus of a hydrogen atom?

(b) What is the electric potential energy U in electron-volts of an electron at the given distance from the nucleus?

(c) If the electron moves closer to the proton, does the electric potential energy increase or decrease?

Sol:

X V x X

r

V e 6.78

10 12 . 2

) 10 60 . 1 )(

10 99 . 8 ( 4

1

10 19 9

0

=

=

= ₋ ⁻

(a) πε

(b)U=qv=(-1.60X10^-19)(6.78)=-6.78eV (c) Decreases V=

∑

∑

= n

i i

i

r q r e

0 1

4 1

πε (n point charge)

= i 1

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The potential at the center of a uniformly charged circular disk of radius R=3.5cm is V0=550V (a) What is the total charge q on the disk?

(b) What is the potential at a point on the axis of the disk a distance Z=5.0R from the center of the disk?

Sol:

(a)Z=0, V0= 2ε0

σ_{R Æ}

R V₀ 2ε0

σ =

q=σ(πR²)=2πε₀RV₀ =1.1nC

(b)Z=5.0RÆV= ( (5.0r) R 5.0R) 54V 2

2 2 0

=

− ε +

σ

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Exercises:24,41,53