ELECTRICITY & MAGNETISMCHAPTER 8

E & M - Focus

Electric Charge & Force

Current, Voltage& Power

Magnetism

Simple Electrical Circuits

Voltage & Current Transformation

Electromagnetism

Electric Charge & Force

Fg = Gm1m2

r2Fe = k

q1q2r2

Gravitational Case Electrical Case

Only One Kind of Mass

Unlike Charges

Like Charges+

+

-

+

Electric Current, IVehicle “current” Electric current

current = kg (mass of vehicles)time

current = chargetime

I = qt

amperes = coulombssecond

Electric Potential Energy - VGravitational Case Electrical Case

h

w

Fg is assumed to be constant Fe is not constantm

dFe

Fe

q1

q2

PEg = wh = mgh V = Wq

volts = joulescoulomb

Batteries - Sources of Voltage

1.5V+ -

q

Move charge q from one battery pole to another. How much work did you do?

-

W =Vq

Note that is does not matter what path the charge goes through!

Electrical Resistance - R• Conductors support high

electric currents becauseof mobile electrons.

• Semiconductors have fewmobile electrons.

• Insulators have no mobileelectrons.

• Conductors have low (but not zero) resistance.

• Semiconductors have highresistance.

• Insulators have infinite resistance.

Resistance - Gravity CaseThese guys are doingwork against gravity,but their also doing work against friction.

h

Electrical Resistance - R

Circuit Elements

Electrical Resistance - RR = V

Iohms = volts

amp

The vulture is above the rabbit.

The vulture is above the iguana.

The iguana and the rabbit are on the same level.

R = VI

I = VR

V = IR

Electrical Power - PPower = Work

Timewatts = joules

second

I = qt

, V = Wq

Recall the equations for I and V

P = Wt

…and so, rearranging things IV = qtWq

= Wt= P

P = IV

Electrical Power - P

P = IVFrom

And V = IR

We get P = I 2R

VR= I

P = IV

P = V2

R

Simple Electrical Circuits

Series

Parallel

But First - Gravity!

h

h1

h2

h3

Key Points:• The flow of water through each wheel is the same.• The total potential energy drop ∝ h = h1 + h2 + h3

Series waterwheels

But First - Gravity

h

Key Points:• Water flow is split unevenly over 3 wheels. Cw = C1 + C2 + C3• The total potential energy drop, h is the same for each wheel.

Parallel waterwheels

C1 C2 C3Cw

C1 C2 C3

Series Electrical Circuit

V = IR V1 = IR1V2 = IR2V3 = IR3

V1 +V2 +V3 =V = IR1 + IR2 + IR3V = I R1 + R2 + R3( )

Req = R1 + R2 + R3 + ...

We know and so,

Equivalent series resistance:

Parallel Electrical Circuit

I = VR

I1 =VR1

I2 =VR2

I3 =VR3

1Req

= 1R1

+ 1R2

+ 1R3

+ ...

We know

and

so,Equivalent parallelresistance:I1 + I2 + I 3 = I =

VR1

+ VR2

+ VR3

I =V 1R1

+ 1R2

+ 1R3

⎛⎝⎜

⎞⎠⎟

Batteries in Series

1.5V+ - 1.5V+ - 1.5V+ -

Total = 4.5 V

Batteries in series can supply 3 times the voltage at the same current.

Batteries In Parallel1.5V+ -

1.5V+ -

1.5V+ -

Total = 1.5 V

Batteries in parallel can supply3 times the current at the samevoltage.

MAGNETISM

Magnetite, or Loadstone

Early MagnetiteCompass

Gravity, Electric AnalogiesGravity Electricity Magnetism

• Only one kind of mass

• Attractive only

• Two kinds of charge, + and -

• Opposites attract, Like charges repel.

• There are no magnetic charges, only fields!

• Opposite poles attract, Like poles repel.

Background - Earth Magnetism

• Geomagnetism:Magnetite Compasswas used for navigation.

• Paleomagnetism:Most rocks have residualmagnetism from the timeof their solidification.

The Magnetic Field

• Tiny “test” compasses could be used to “map” a magnetic field.

Also:• You could do this

with a test mass to map a gravitational field.

• You could do this with a test charge to map out and electric field.

Thought Experiments:

Electric Current & Magnetic Field

R (wire)

V+-

I

MagneticField

A flow of electric current comes with a magnetic field.

Moving charge creates a magnetic field.

Electric Current & Magnetic Field

R (wire)

V+-

I

MagneticField

In a loop, the magnetic field becomes more concentrated at the center.

Electric Current & Magnetic FieldIn a coil, the magnetic field becomes even more concentrated at the center.

R (wire)V+-

I

MagneticField

N

S

Right Hand Rule for IIf your right thumb points in the direction of conventional current, then your fingers point in the direction of the magnetic field (B-field).

Magnetic Force On Moving Charges

• Relative motion between the magnetic field and the charge is what counts.

• For negative charges (electrons) use you left hand.

• If a conductor is passed though a magnetic field, a current can flow!

Electrical Generation

Changing Magnetic FieldA changing magnetic field can also

induce electric currents.

I

Alternating Magnetic

Field

R, load

IOutput from AC generator on previous slide

This induced current can drive a useful electrical device.

The Transformer

V

V2 =N2

N1

⎛⎝⎜

⎞⎠⎟V1

I2 =N1N2

⎛⎝⎜

⎞⎠⎟V1

Transformers are used to change voltage and current levels in practical power distribution networks.

P2 = I2V2 =N1N2

⎛⎝⎜

⎞⎠⎟I1

N2

N1

⎛⎝⎜

⎞⎠⎟V2 = I1V1

P2 = P1

Note: Power is conserved

The Power Grid