Physics 213General Physics

Lecture 2

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Last Meeting: Electric Charge, Conductors/Insulators

Today: Static Charges, Conductors, Coulomb’s Law, Electric Forces, Electric Field

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Demo

Glass, Silk, Amber, Fur, Tape conduction/induction

Comb and PaperPivoting PlankVan de Graaff Generator

Van de GraaffGenerator

Charge is transferred to the dome by means of a rotating belt

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Charging by Conduction

A charged object (the rod) is placed in contact with another object (the sphere)

Some electrons on the rod can move to the sphere

When the rod is removed, the sphere is left with a charge

The object being charged is always left with a charge having the same sign as the object doing the charging

Charging by Induction

• When an object is connected to a conducting wire or pipe buried in the earth, it is said to be grounded

• A neutral sphere has equal number of electrons and protons

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Polarization

In most neutral atoms or molecules, the center of positive charge coincides with the center of negative charge

In the presence of a charged object, these centers may separate slightly This results in more positive charge on

one side of the molecule than on the other side surface of the insulator

This realignment of charge on the surface of an insulator is known as polarization

A charged comb attracts bits of paper due to polarization of the paper

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Vector Nature of Electric Forces

Two point charges are separated by a distance r

The like charges produce a repulsive force between them

The force on q1 is equal in magnitude and opposite in direction to the force on q2

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Vector Nature of Forces, cont.

Two point charges are separated by a distance r

The unlike charges produce a attractive force between them

The force on q1 is equal in magnitude and opposite in direction to the force on q2

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Vector Nature of Electric Forces

Magnitude of the force

In the direction of

The precise Coulomb’s law

1 22

| || |q qF k

r

1 212 2

q qF k

r

12r 12r

1 212 122 12ˆ ˆ ( is a unit vector)r

q qF k r

r

21 12r r

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Unit Vectors

A unit vector is a dimensionless vector with a magnitude of exactly 1.

Unit vectors are used to specify a direction Reference: Serway and Vuille, 8th ed.

Chapter 3.

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Unit Vectors, cont.

The symbols

represent unit vectors They form a set of

mutually perpendicular vectors

Right-hand convention

ˆˆ ˆ, ,i j and k

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Unit Vectors in Vector Notation

Ax is the same as Ax and Ay is the same as Ay etc.

The complete vector can be expressed as

i

j

ˆ ˆ ˆx y zA A A A i j k

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Adding Vectors Using Unit Vectors

Using R = A + BThen

and so Rx = Ax + Bx and Ry = Ay + By

ˆ ˆ ˆ ˆ

ˆ ˆ

x y x y

x x y y

x y

A A B B

A B A B

R i j i j

R i j

R R R

2 2 1tan yx y

x

RR R R

R

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Vector Nature of Forces, cont. Two point charges are

separated by a distance r The unlike charges

produce an attractive force between them

The force on q1 is equal in magnitude and opposite in direction to the force on q2

pair)reaction -(action ˆˆ 21221

2112221

12 rr

qqkFr

r

qqkF

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Four point charges, each of the same magnitude, with varying signs are arranged at the corners of a square as shown. Which of the arrows labeled A, B, C, and D gives the correct direction of the net force that acts on the charge at the upper right corner?a. A

b. Bc. Cd. De. The net force on that charge is zero

Answer: b

Question:

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20

3

1

2

Answer:4

Consider first the force from 1 on 4.

We will now do the forces from the other charges on 4.We can add up all three force vectors to determine the net force on 4.

21

3

1

2

Answer:

2

1 2

2

2 2

3 2

2

3 3 2

2

3 3 2

1 3

2 3

in the direction D2

1cos 45

2 2

1sin 45

2 20

0

The answer is B.

x

y

x

y

x x x

y y y

QF k

a

QF k

aQQ

F ka

QF F k

a

QF F k

a

F F F

F F F

Superposition Principle

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22

221

rmm

GF

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Q

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Faraday introduced electric field and electric field lines which are said to exist in the region of space around a charged object. When another charged object enters this electric field, the field exerts a force on the second charged object

2| ( ) |

qE r k

r

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Coulombs force and electric fields.

12221

12 rrqq

kF

12221

12 rrqq

kF

1221

1 rrq

kE

q1q2 qtest

q3q4

Superposition Principle

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Direction of Electric Field

The electric field produced by a negative charge is directed toward the charge A positive test

charge would be attracted to the negative source charge

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Direction of Electric Field, cont

The electric field produced by a positive charge is directed away from the charge A positive test

charge would be repelled from the positive source charge

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An electron traveling horizontally enters a region where a uniform electric field is directed upward.What is the direction of the force exerted on the electron once it has entered the field?

(a) to the left

(b) to the right

(c) upward

(d) Downward

(e) out of the page, toward the reader

Answer: d

Question:

Rules for Drawing Electric Field Lines1. The lines for a group of charges must begin on

positive charges and end on negative chargesIn the case of an excess of charge, some lines will begin or

end infinitely far away

2. The number of lines drawn leaving a positive charge or ending on a negative charge is proportional to the magnitude of the charge

3. No two field lines can cross each other4. The net number of lines at infinite distance is

proportional to the net charge in the system.

Electric Field Line Patterns

Point charge

The lines radiate equally in all directions

For a positive source charge, the lines will radiate outward

Electric Field Line Patterns

For a negative source charge, the lines will point inward

Electric Field Line Patterns

An electric dipole consists of two equal and opposite charges

The high density of lines between the charges indicates the strong electric field in this region

Electric Field Line Patterns

Two equal but like point charges

At a great distance from the charges, the field would be approximately that of a single charge of 2q

The bulging out of the field lines between the charges indicates the repulsion between the charges

The low density of field lines between the charges indicates a weak field in this region

Electric Field Patterns

Unequal and unlike charges

Note that two lines leave the +2q charge for each line that terminates on -q