# shows0 volts for

each channel

screen menu,calcs & info

menu buttons

cursorcontrol

cursor

triggeringcontrol

usualchannelcontrols

measure

autoset

# shows0 volts for

each channel

screen menu,calcs & info

menu buttons

cursorcontrol

cursor

triggeringcontrol

usualchannelcontrols

measure

autoset

B

BB

B

Boutside=0 Boutside=0

uniformmagnetic

field inside

Ideal Solenoid

BIN

Use Ampere’s Lawto Find Magnetic Field

Am

peria

n Lo

op

L

B d

s

whole loop

oItotalenclosed

B d

s

insidesolenoid

oNI

Bindy0

L oNI

Bin dy0

L oNI

BinL oNI

Bin oNI

LBin onIN solenoid loops

enclosed, eachwith current I.

where n is “loop density” N/L of solenoid.

(Explain each step in your report.)

voltage

t

VR=RIR=RIL

Bampere

L

The current in the solenoid creates a magnetic field inside the solenoid due to Ampere’s Law.

The changing magnetic field inside the solenoid causes a back EMF (voltage) due to Faraday’s Law. Notice that dI/dt causes a phase shift.

Direction of currentinside the resistor?

NS

velocity

R

B

dB

dt 0Inside the solenoid:

NS

velocity

R

B Binduced

I

ReceiverTransmitter

Oscillating voltagereceived is measurable.

Oscillating transmittingmagnetic fields.

Oscillating transmitting voltage.

Transmitting magnetic fields reach inside coils.

voltage

The LRC Circuit - AC Driven

VLVC

VR

voltage

The LRC Circuit - AC Driven: Source from Addition

VLVC

VR

Vsource

A B C

0.1 F50 mH

100

Iamplitude

fdrive

fresonance

Iamplitude

fdrive

fresonance

Large R Small R

VR(t)

VS(t)

VR(t)

VS(t)

out of phase in phase

45o

(r) A

r

System: Charged hollow spherewith inner radius a and outer radius b.

Charges: nonuniform charge distribution in between (so not a conductor):

Problem solving strategy: 1) Draw non-physical Gaussian sphere at distance r where you want to find Er. 2) Use Gauss’s law to write equation for Er in terms of other parameters. 3) Solve for Er. In this case solve in 3 places, inside hollow region (rI), inside charged region (r2) and outside (r3).

rI

r2

r3

Problem: The electric field is a radial vectorfield due to the symmetry of thesystem. Findthe electricfield magnitudein the radial direction atevery distancefrom the origin.

dQcharge

dVvolume

d sind r2dr

0

0

2

4 A

r

r2dr

4 Ardr

Required vectorcalculus knowledge:

(r) Ar

System: Charged infinite cylinder with radius a.

Charges: Nonuniform charge distributioninside cylinder (so not a conductor):

rI

r2

Problem: The electric field is a radial vector field dueto the symmetry of thesystem. Find theelectric field magnitudein the radial directionat every distancefrom the origin.

dQcharge

dVvolume

d dz rdr

0

2

(hmm...)

Required vector calculus knowledge:

dQcharge

dVvolume

d dz rdr

0

zo

0

2

2zo Ar rdr

2zo Ar2dr

Try solving over a finite height zo:

Problem solving strategy: 1) Draw non-physical Gaussian cylinder at distance r where you want to find Er. 2) Use Gauss’s law to write equation for Er in terms of other parameters including an arbitrary height zo. 3) Solve for Er. In this case solve in 2 places, inside region (rI), and outside (r2). You will need to have the arbitrary height zo cancel in the end.

zo

Another view of drawing a Gaussian cylinder of radius r andfinite length zo around an infinite cylinder of charge (this one outside).

r

System: Charged infinite slab of width w in x-y direction.

Charges: Uniform slab of charge density :

Problem: The electric field is a vector fieldpointing perpendicular to the plane of the slabdue to the symmetry of the system. Find theelectric field magnitude in the perpendiculardirection at a given distance from the middleof the slab.

dQcharge

dVvolume

dx dy dz

(hmm...)

Required vector calculus knowledge:

dQcharge

dVvolume

dx dy dz0

z

0

yo

0

xo

xoyo dz0

z

Try solving over a finite box xo and yo:

Problem solving strategy: 1) Draw non-physical Gaussian rectangular prism from center of slab to height z where you want to find Ez. 2) Use Gauss’s law to write equation for Ez in terms of other parameters including arbitrary length and width xo and yo. 3) Solve for Er. In this case solve in 2 places, inside region (zI), and outside (z2). You will need to have the arbitrary xo and yo cancel in the end.

Set z=0 in middle of slab.

z2

xo

yo

z1

xo

yo

V V

Three representations of the same circuit:

BA

TT

ER

Y

+

BA

TT

ER

Y

+

BA

TT

ER

Y

+

BA

TT

ER

Y

+

V

3.0

Circuit Position0

(Note: bulb shape

distorted.)

3 V

b

c

d

3 V

a b

c

d

BA

TT

ER

Y

+

BA

TT

ER

Y

(Note: bulb shape

distorted.)

c d

BA

TT

ER

Y

+

BA

TT

ER

Y

+a b

c

d

1.5 V1.5 V

1.5 V

1.5 V

1.5 V

A. B. C.

1.5 V1.5 V

1.5 V

A. B. C.

1.5 V1.5 V

1.5 V1.5 V

1.5 V

A. B. C. D.

1.5 VV1.5 V

V+

-

+

-V

+

-

BA

TT

ER

Y

+

BA

TT

ER

Y

+

ITOTAL

IA IB IC

IE

ID

BA

TT

ER

Y

+

BA

TT

ER

Y

+

BA

TT

ER

Y

+

BA

TT

ER

Y

+

BA

TT

ER

Y

+

3 V

Voltage

VDC

Measuring the voltage drop across a light bulb (DMM in parallel):

VR

BA

TT

ER

Y

+

Amperes

mA

Measuring the voltage drop across a light bulb (DMM in series):

A

R

BA

TT

ER

Y

+

Ohms ()

Measuring the resistance of a light bulb (component disconnected):

R

BA

TT

ER

Y

+

V

1.5

Circuit Position0

BA

TT

ER

Y

+

V

1.5

Circuit Position

Thumb pointsto North

Right-hand-wrap rule for finding direction of magnetic poles created by moving charges (current).

N

S

Wrap fingersin direction ofcurrent. q

If charge is negative,reverse poles.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

N

S

N

S

N

S

S

S

SMAGNETIC

NMAGNETIC

N

S

++

+

+

++ +

+

+

+

+

+++

Excess positive charge on the surface of a spherical conductor.

-

-

-

Excess negative charge onthe surface of a cubic conductor.

-

-

--

-

-

--

-

-

- --

-

-

-

--

- ---

-

--

-

-

(Excess charges always repel each other to the surface.)

+

++

+

++

+ - Negatively charged attracts positive charge and repels negative charges on the surface of a conductor.

+---- --

-

---

---

+Positively charged object creates an electric field that rotates polar molecules in insulator.

+-MAGNIFY

insulator/dielectric material

rotate

+-

+-

Electrons deposited on the surface of a balloonby rubbing it against your hair do not spread out.

--

---

-- -

-