Physics II: Electricity & Magnetism

Physics II:Electricity & Magnetism

Physics II:Electricity & Magnetism

Section 21.11Section 21.11

Thursday (Day 16)Thursday (Day 16)

Warm-UpWarm-Up

Thurs, Feb 12

Complete Graphic Organizers for Sections 21-8 & 21-10.

Place your homework on my desk: “Foundational Mathematics’ Skills of Physics” Packet (Page 18) Web Assign 21.12 - 21.14

For future assignments - check online at www.plutonium-239.com

Thurs, Feb 12

Complete Graphic Organizers for Sections 21-8 & 21-10.

Place your homework on my desk: “Foundational Mathematics’ Skills of Physics” Packet (Page 18) Web Assign 21.12 - 21.14

For future assignments - check online at www.plutonium-239.com

Essential Question(s)Essential Question(s) WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE

NECESSARY IN PHYSICS II? HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS

AND APPLY IT TO VARIOUS SITUATIONS?How do we compare and contrast the basic properties of an

insulator and a conductor?How do we describe and apply the concept of electric field?

WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?How do we compare and contrast the basic properties of an

insulator and a conductor?How do we describe and apply the concept of electric field?

VocabularyVocabulary Static Electricity Electric Charge Positive / Negative Attraction / Repulsion Charging / Discharging Friction Induction Conduction Law of Conservation of Electric

Charge Non-polar Molecules

Static Electricity Electric Charge Positive / Negative Attraction / Repulsion Charging / Discharging Friction Induction Conduction Law of Conservation of Electric

Charge Non-polar Molecules

Polar Molecules Ion Ionic Compounds Force Derivative Integration (Integrals) Test Charge Electric Field Field Lines Electric Dipole Dipole Moment

Polar Molecules Ion Ionic Compounds Force Derivative Integration (Integrals) Test Charge Electric Field Field Lines Electric Dipole Dipole Moment

Foundational Mathematics Skills in Physics Timeline

Foundational Mathematics Skills in Physics Timeline

Day Pg(s) Day Pg(s) Day Pg(s) Day Pg(s)

11

26 3 11 16 16 21

213

147 4 12 17 17 8

322

238 5 13 18 18 9

424

†129 6 14 19 19 10

5 15 10 7 15 20 20 11

WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

AgendaAgenda

Review “Foundational Mathematics’ Skills of Physics” Packet (Page 18) with answer guide.

Discuss Torque, factors that affect torque, r X F Electric Dipoles Electric Dipoles in an Electric Field The electric field produced by a dipole Calculations: Dipoles in an electric field

Review “Foundational Mathematics’ Skills of Physics” Packet (Page 18) with answer guide.

Discuss Torque, factors that affect torque, r X F Electric Dipoles Electric Dipoles in an Electric Field The electric field produced by a dipole Calculations: Dipoles in an electric field


How do we compare and contrast the basic properties of an insulator and a conductor?What are characteristics and classification(s) of

electrically . . .conductive atoms?insulative atoms?semi-conductive atoms?conductive compounds?insulative compounds?semi-conductive compounds?

How do we compare and contrast the basic properties of an insulator and a conductor?What are characteristics and classification(s) of

electrically . . .conductive atoms?insulative atoms?semi-conductive atoms?conductive compounds?insulative compounds?semi-conductive compounds?


How do we describe and apply the concept of electric field?How do we calculate the net force and torque

on a collection of charges in an electric field?

How do we describe and apply the concept of electric field?How do we calculate the net force and torque

on a collection of charges in an electric field?

How do we calculate the net force and torque on a collection of charges in an electric field?

TorqueTo make an object start rotating, a force is needed; the position and direction of the force matter as well.

The perpendicular distance from the axis of rotation to the line along which the force acts is called the lever arm.


Torque

A longer lever arm is very helpful in rotating objects.


Torque

Here, the lever arm for FA is the distance from the knob to the hinge; the lever arm for FD is zero; and the lever arm for FC is as shown.


Torque

The torque is defined as:

= rF

or

= r F

Torque, Torque, Torque is perpendicular to the direction of the rotation. Right-hand rule - The direction of the positive torque is

in the direction of increasing angle) In general, if we define torque as

= r x F = r F sin Also, torque can be defined about any point using

net = (ri x Fi) where ri is the position vector of the ith particle and Fi is

the net force on the ith particle.

Torque is perpendicular to the direction of the rotation. Right-hand rule - The direction of the positive torque is

in the direction of increasing angle) In general, if we define torque as

= r x F = r F sin Also, torque can be defined about any point using

net = (ri x Fi) where ri is the position vector of the ith particle and Fi is

the net force on the ith particle.


Bond Types (Revise)Bond Types (Revise)

Covalent: share electrons equallyIonic Transfer electrons (each ion has

full charge)Polar covalent: share electrons

unequally (both atoms that make up the bond have a slightly positive or negative charge - they do not have full charge)

Covalent: share electrons equallyIonic Transfer electrons (each ion has

full charge)Polar covalent: share electrons

unequally (both atoms that make up the bond have a slightly positive or negative charge - they do not have full charge)

Electronegativity ActivityElectronegativity Activity

I.e. similar to organic chemistry Section 1.10?

I.e. similar to organic chemistry Section 1.10?

Electric DipolesElectric Dipoles

•The combination of two equal charges of opposite sign, +Q and -Q , separated by a distance l, is referred to as an electric dipole. The quantity Ql is called the dipole moment, p. The dipole moment points from the negative to the positive charge. Many molecules have a dipole moment and are referred to as polar molecules. •It is interesting to note that the value of the separated charges may be less than that of a single electron or proton but cannot be isolated.


Electric DipolesElectric Dipoles

• Electric Dipoles: The combination of two equal charges of opposite sign, +Q and -Q, separated by a distance l. • The dipole moment, p: The quantity Ql. • The dipole moment points from the negative to the positive charge. • Many molecules have a dipole moment and are referred to as polar

molecules. • It is interesting to note that the value of the separated charges may be less

than that of a single electron or proton, but they cannot be isolated.

• Electric Dipoles: The combination of two equal charges of opposite sign, +Q and -Q, separated by a distance l. • The dipole moment, p: The quantity Ql. • The dipole moment points from the negative to the positive charge. • Many molecules have a dipole moment and are referred to as polar

molecules. • It is interesting to note that the value of the separated charges may be less

than that of a single electron or proton, but they cannot be isolated.

Relating Induced Electric Dipole to Dipole MomentsRelating Induced Electric Dipole to Dipole Moments

Dipole in an External FieldDipole in an External Field


F±

-q

+q F+

F±

F−

A dipole, p = Ql, is placed in an electric field E. First, let us analyze the angle , for torque and about its bisector at point O.

Point O sinPoint O F± sinF±

0° 180°

45° 135°

90° 90°

135° 45°

180° 0°

0 0

22

22

1 1

22

22

0 0

Note that the choice of the angle does not change our value for sin point O will be used for all reference angles instead of the rxF angle to relate the direction of the dipole moment to the E-Field.


A dipole, p = Ql, is placed in an electric field E. Next, let us analyze the direction of the torque force to the change angle , Note: By definition, positive torque always increases the value of (I.e. move the dipole in the counterclockwise direction).


It is also important to note that the applied torque force will cause the angle decrease (in the clockwise direction) instead of increase (counter-clockwise) about point O. about point O is negative.


A dipole p = Ql is placed in an electric field E.


=r × F =rF sinθ

net = r × F∑ = rF sinθ∑=rF+ sinθ + rF− sinθ

net =l

2QE( )sinθ +

l

2QE( )sinθ

net = QlE sinθ =pE sinθ =p × E

net = τ + + τ −


The effect of the torque is to try to turn the dipole so p is parallel to E. The work done on the dipole by the electric field to change the angle from to , is

W = d

∫Because the direction of the torque is opposite to the direction of increasing , we write the torque as

Then the dipole so p is parallel to E. The work done on the dipole by the electric field to change the angle from to , is

=−p × E or τ = − pE sinθ

W =−pE sin d

∫ =pE cosθθ1

θ2 =pE cosθ2 − cosθ1( )



Positive work done by the field decreases the potential energy, U, of the dipole in the field. If we choose U = 0 when p is perpendicular to E (that is choosing = 90º so cos = 0), and setting = then

W =pE cos

={ −cos

⎛

⎝⎜

⎞

⎠⎟ =pE cosθ

U =−W =−pE cosθ =−p ⋅E


+

+

–



W =pE cos

={ −cos

⎛

⎝⎜

⎞

⎠⎟ =pE cosθ



++ –



W =pE cos

={ −cos

⎛

⎝⎜

⎞

⎠⎟ =pE cosθ



++–

Torque with respect to the Dipole’s Orientation

Torque with respect to the Dipole’s Orientation


Electric Field Produced by a Dipole


To determine the electric field produced by a dipole in the absence of an external field along the midpoint or perpendicular bisector of the dipole.

hh hr

–

+

h = r + L 4 E =E+ +E−


E+ = E− =E =1

4πε 0

Q

h2

Enet =E+ cos + E−cos =2E cosθ =2EL

2r2 + L2 4

Enet =EL

r + L 4=

1

4πε 0

Q

r2 + L2 4( )

L

r2 + L2 4

Enet =

4πε0

p

r + L 4( )3

Enet =

4πε0

pr3 at r >> L



It is interesting to note that at r >> l, the electric field decreases more rapidly for a dipole (1/r3) than for a single point charge (1/r2). This is due to the fact that at large distances the two opposite charges neutralize each other due to their close proximity At distances where r >> l, this 1/r3 dependence also applies for points that are not on the perpendicular bisector of the dipole.

E =

4πε0

pr3 For a dipole at r >> l

hh hr

–

+

E =

4πε0

qr For a single point charge


∝1

r3

∝1

r2

Table of Dipole Moment Values

Table of Dipole Moment Values


Dipoles in an Electric FieldDipoles in an Electric Field

The dipole moment of a water molecule is 6.1 x 10-30 C•m. A water molecule is placed in a uniform electric field with magnitude 2.0 x 105 N/C.

• What is the magnitude of the maximum torque that electric field can exert on the molecule?

• What is the potential energy when the torque is at its maximum?

• What is the dipole moment, p1 and p2, for a single O-H bond (where 2 = 104.5°)? Note: Let


max = p × E =pE sin θ

=90°}

=1{ =pE

= 6.1 x 10−30 Cgm( ) 2.0 x 105 N

C( ) =1.2 x 10−24 Ngm

U =−p⋅E =−pE cosθ =−pE cos 90o( ) =0

p1 =p =pOH .

p1 cos

p2 cos

p =pnet =p1 cosθ + p2 cosθ =2 pOH cos θ 2( )

⇒ pOH =p

2cos θ 2( ) =

6.1 x 10−30 Cgm( )

2 cos 104.5° 2( ) = 4.98 x 10−30 Cgm


The dipole moment of a water molecule is 6.1 x 10-30 C•m. A water molecule is placed in a uniform electric field with magnitude 2.0 x 105 N/C.

• In what position will the potential energy take on its greatest value?

• Why is this different than the position where the torque is maximized?

The potential energy will be maximized when cos = –1, so = 180°, which means p and E are antiparallel. The potential energy is maximized when the dipole moment is oriented so that it has to rotate through the largest angle, 180°, to reach equilibrium at = 0°.

The torque is maximized when the electric forces are perpendicular to p.



The carbonyl group (C=O) dipole. The distance between the carbon (+) and oxygen ( –) atoms in the carbonyl group which occurs in many organic molecules is about 1.2 x 10-10 m and the dipole moment of this group is about 8.0 x 10-30 C•m. A formaldehyde molecule, CH2O, is placed in a uniform electric field with magnitude 2.0 x 105 N/C.

• What the direction of the dipole moment, p?

• What is the magnitude of the maximum torque that electric field can exert on the molecule?

• What is the potential energy when the torque is at its maximum?


p

max = p × E =pE sin θ

=90°}

=1{ =pE

= 8.0 x 10−30 Cgm( ) 2.0 x 105 N

C( ) =1.6 x 10−24 Ngm

U =−p⋅E =−pE cosθ =−pE cos 90o( ) =0



• What is the partial charge (±) of the carbon (+) and oxygen ( –) atoms in the carbonyl group?

• (a) How much of the quantized charge of an electron/proton is the partial charge of the carbonyl group to? (b) What is this value in percent?

p =Ql ⇒ Q =p

l =

8.0 x 10−30 Cgm( )

1.2 x 10−10 m( )= 6.7 x 10−20 C

(a)n =

Qδ±

Q±

=0.42


(b) Percentage of an electron's charge =nx00%=.42 x 100% = 42%



• In what position will the potential energy take on its greatest value?

• Why is this different than the position where the torque is maximized?

The potential energy will be maximized when cos = –1, so = 180°, which means p and E are antiparallel. The potential energy is maximized when the dipole moment is oriented so that it has to rotate through the largest angle, 180°, to reach equilibrium at = 0°.

The torque is maximized when the electric forces are perpendicular to p.


SummarySummary

How does positive torque relate to the change in the angle?

HW (Place in your agenda): “Foundational Mathematics’ Skills of Physics” Packet (Page 19) Web Assign 21.15

Future assignments:

How does positive torque relate to the change in the angle?

HW (Place in your agenda): “Foundational Mathematics’ Skills of Physics” Packet (Page 19) Web Assign 21.15

Future assignments:


Supplementary NotesSupplementary Notes

Vector Cross ProductVector Cross Product

Known as the vector product or cross product

The cross product of two vectors A and B is defined as another vector C = A x B whose magnitude is C = |A x B| = AB sin where < 180º between A and B and whose direction is perpendicular to both A and B.

Right hand rules for cross products

Known as the vector product or cross product

The cross product of two vectors A and B is defined as another vector C = A x B whose magnitude is C = |A x B| = AB sin where < 180º between A and B and whose direction is perpendicular to both A and B.

Right hand rules for cross products

Vector Cross ProductVector Cross Product

The cross product of two vectors A = Axi + Ayj + AzkB = Bxi + Byj + Bzk

Can be written as

A x B = (AyBz-AzBy)i + (AzBx-AxBz)j + (AxBy-AyBx)k

The cross product of two vectors A = Axi + Ayj + AzkB = Bxi + Byj + Bzk

Can be written as

A x B = (AyBz-AzBy)i + (AzBx-AxBz)j + (AxBy-AyBx)k

€

A × B =

i j k

Ax Ay Az

Bx By Bz

Properties of Vector Cross Products

Properties of Vector Cross Products

A x A = 0A x B = -B x A A x (B + C) = (A x B) + (A x C) .

A x A = 0A x B = -B x A A x (B + C) = (A x B) + (A x C) .

€

d

dtA × B( ) =

dA

dt× B + A ×

dB

dt

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Physics II: Electricity & Magnetism