chapter 17 electric charge and electric field. two kinds of charges: positive and negative two...

Chapter 17

Electric Charge and Electric Field

Two kinds of charges: positive and negative

• Two charges of the same kind REPEL each other

• Two charges of different kinds

ATTRACT each other

Coulomb’s Law

• The magnitude F of the force that each of two point charges q1 and q2 exerts on each

other when they are separated by a distance r is directly proportional to the product of the two charges and inversely proportional to the distance squared

F = k |q1q2|/r2

q1 q2

Additive forces

q3

r12 r23

r13

ELECTRIC FIELD

GAUSS’s LAW

The total flux ΦE coming out of any closed surface is proportional to the total electric charge Qencl inside the volume surrounded by this surface.

ΦE = Qencl / ɛo

Ɛo = 8.854x10-12C2/(N.m2)

Chapter 18

Electric Potential and Capacitance

ELECTRIC POTENTIAL ENERGYElectric potential energy is between two

charges (q and q’ ) separated by a distance r and is defined as:

PE = kqq’/r

Electric potential energy is a scalar and has units of Joule (J).

When there are more than 2 charges, the total potential energy is the sum of the energy associated with each pair of charges

• In the gravitational case, the change in the potential energy associated with an object with mass m when moved from the surface to a height h is

mgh

Similarly, the electric potential energy associated with a charge q in a field E is:

qEd

When the charge is moved a distance d along or opposite direction of the field

ELECTRIC POTENTIAL or VOLTAGE

• A charge Q creates an electric field around it.

Similarly, this charge will create an electric potential V around it, commonly called voltage

It is a scalar and is defined as:

V = kQ/r

The unit for electric potential is the Volt (V).

Consequently, when a charge q is placed at a distance r from Q, the electric potential energy between the two charges would be:

U = qV

ELECTRIC POTENTIAL and ELECTRIC FIELD

• For parallel plates separated by a distance d

and a potential difference between them V

the field between the plates is then:

E= V/d

Or

V=Ed

DEFINITION

• The CAPACITANCE C of a capacitor is the ratio of the magnitude of the charge Q on either conductor (plate) to the magnitude of the potential Vab between the conductors (plates):

C =Q/Vab

The SI unit of capacitance is FARAD

(1farad = 1C/1V)

CAPACITANCE FOR PARALLEL PLATES

• If the capacitor is made of parallel plates with surface area A and a separation d between the plates, the capacitance is:

C = ɛ0A/d

Capacitors are often joined

Capacitors are often joined II – Figures 18.22

Electric Field Energy in a Capacitor

• One of the applications of the capacitor is to store energy (analogous to the potential energy stored in a spring)

Ucapacitor = (1/2) CV2

Chapter 19

Current, Resistance, and Directed-Current Circuits

Current defined

Unit: 1coulomb/second = 1 ampere = 1A

Resistance and Ohm’s Law

• When the potential difference V between the two ends of a conductor is proportional to the current I passing through the conductor, the ratio (V)/(I) is called the resistance of the conductor :

R = V/IThe SI unit for resistance is the ohm and it is

represented by the Greek letter Ω 1Ω = 1V/A

Resistivity• The resistance is the property of a given conductor and

it depends on its length L and cross- section area A

L

R = ρ L/A

ρ characterizes the conduction properties of the material

Power in Electric Circuit

The power P is defined as

P = VabI

The unit for power is the watt1W = 1J/s

Power for a pure resistor:

For a pure (single) resistor, we have:

P=VabI

Since V= RI

P = RI2 or P = V2ab/R

Connections in series

Req = R1 + R2 + R3

SAME CURRENTDIFFERENT POTENTIAL

Connections in parallel

1/Req = 1/R1 + 1/R2 + 1/R3

SAME POTENTIALDIFFERENT CURRENT

Chapter 20

Charges moving with respect to a field

Charges moving with respect to a field

Charges moving with respect to a field

UNIT FOR MAGNETIC FIELD• The magnetic field B has unit, in SI :

TESLA

1 tesla = 1T=1N/(A.m)

The effect of the sign of a moving charge

Magnetism and circular motion

F = |q|vB

If the motion is Circular

F = mv2/R

R = mv/ |q|B

ω = v/R = |q|B/m

Force on a conductor with current

F = ILB

The motor and torque

= (IaB)bsinΦ

Magnetic field of long straight conductor

Magnetic field of a long, straight wire:

B = μ0I/(2πr)

r is the distance from the wire μ0 is called the permeability of vacuum

μ0 = 4π x 10-7 T.m/A

Fields in two conductors side-by-side

2 wires with currents flowing in the same direction attract each other

2 wires with currents flowing in opposite directions repel each other

F = μ0 L(I1 I2)/(2πr)

Force per unit lengthF/L = μ0 (I1 I2)/(2πr)

Currents in a loop

Magnetic field at the center of a circular loopB = μoI /(2R) For N loops: B = μo NI /(2R)

Magnetic field of a Solenoid: B = μonIn = number of turns per unit lengthn = N/L

SOLENOID

Chapter 21

Electromagnetic Induction

Does the field induce a current or not?

Magnetic flux at various orientations

Magnetic flux at various orientations

Magnetic flux at various orientations

Magnetic flux at various orientations

FRADAY’s LAW• When the magnetic flux ΦB changes in

time, there is a an induced emf directly proportional

to the time rate of change of the magnetic flux :

ɛ = |Δ ΦB /Δt |If we have a coil with N identical turns, then

ɛ = N |Δ ΦB /Δt |

Lenz’s Law

Lenz’s Law

Self-inductance

Transformers

TRANSFORMERSV2 / V1 = N2 / N1

If energy completely transformed

V1I1 = V2I2

Energy associated with an induced current.•energy is stored in an electronic device.

The R-L circuit

The L-C circuit •

In this case, the energy is transferred from the electric field (capacitor) to magnetic field (inductor) and vice versa.

The total energy is however conserved:

The back and forth of the energy constitutes an oscillatory behavior with a frequency ω:

Chapter 22

Alternating Current

• A coil of wire rotating with constant angular velocity in a magnetic field develops a sinusoidal oscillating current.

• The potemtial will vary from a maximum V at a frequency ω (or, by a factor of 2π, as f in Hz).

What are phasors?

• Phasors are graphic representations of location. In two dimensions, you can locate a unique point with a radius vector of length L and its angle with respect to zero.

Resistance and Reactance

VR = RI

Resistance and Reactance – Figure 22.6

Resistance and Reactance – Figure 22.6

An Inductor in a circuit

VL = XLIXL = ωL

An Inductor in a circuit

An Inductor in a circuit –

A capacitor in an AC circuit

VC = XCIXC = 1/ωC

A capacitor in an AC circuit

A capacitor in an AC circuit – Figure 22.8

The series R-L-C circuit

V=ZI

Current and voltage may be found

Current and voltage may be found

Power in AC Circuits

Chapter 23

Electromagnetic Waves

Electromagnetic waves

The electromagnetic wave

The electromagnetic wave• The waves are transverse: electric to magnetic and both to the direction of propagation.

•The ratio of electric to magnetic magnitude is E=cB.

•The wave(s) travel in vacuum at c (speed of light in vaccum).

C = 3.00x108 m/s•Unlike other mechanical waves, there is no need for a medium to propagate.

vwave = λ /T vwave = λ f

for light: c= λ f

Speed of a wave

S = Ɛ0cE2 S = EB/μo

Sav = (1/2) Ɛ0cE2max

Sav = (EmaxBmax)/(2μ0)

The INTESITY of the wave I :I = Sav

Reflection and refraction

Refraction

Definition of Index of Refraction

• The index of refraction of an optical material is

n = c/vWhere c is the speed of light in vacuum and v

the speed of light in the material

The frequency f of the wave does NOT change when moving from one material to

another

λ =λ0/n

Relation between angles

• The angle of reflection θr is equal to the angle of incidence θa for al wavelengths and pair of materials.

• For monochromatic light the angle of refraction θb is related to the angle of incidence θa by:

nasin θa = nbsin θb

With the refracted ray being always on opposite sides of the normal

This is Snell’s Law

To perform calculations, use the data in Table 23.1

Total internal reflection

Sinθcrit = nb/na

Chapter 24

Geometric Optics

Reflections at a plane surfaceReview key terms.

• object

• image

• real

• virtual

• distance to image

• distance to object

• magnification

• upright

• inverted

Sign rules for images and objects

• The position of the object and the image determine sign convention.

• Object distance:

Object same side of reflecting/refracting surface as incoming light: s is positive

image distance:imaget same side of reflecting/refracting surface as outgoing light: s’ is positive

Magnification

m = y’/y = -s’/s

Plane mirrors exhibit left-right reversalHave you ever looked at some emergency service vehicles and

wondered what ECILOP or ECNALUBMA means? (Actually it’s even harder, the letters are reversed in their presentation).

Spherical mirrors• Reflections from a spherical mirror depend on the

radius of curvature.

1/s + 1/s’ = 2/R

Concave spherical mirrors

Concave spherical mirrors

• Focal length: f

f = R/2

Hence:

1/s + 1/s’ = 1/f

The principal rays for mirror imaging

m = y’/y = -s’/s

The convex spherical mirror

The convex spherical mirror

Reflection and production of paraxial rays

Specific ray tracing for mirror analysis

Specific ray tracing for mirror analysis

A complete image construction

A complete image construction

A complete image construction

Refraction at spherical surfaces

(na/s) +(nb/s’) = (nb-na)/R

m = y’/y = -(nas’)/(nbs)

THIN LENSES

The converging lens –

Converging lensf > 0

The principal rays for thin lenses

The converging lens –

Diverging lensf < 0

Diverging lenses and foci

Diverging lenses and foci

The principal rays for thin lenses

Any lens that is THICKER in the center than the edges is a converging lens with POSITIVE f

Any lens that is THINNER in the center than the edges is a diverging lens with NEGATIVE f

We assume that the index of refraction of the lens is greater than surrounding one.

Equations for thin lenses

(1/s) + (1/s’) = (n-1)[(1/R1) – (1/R2)]

(1/f) = (n-1)[(1/R1) – (1/R2)]

This is the lensmaker equation

R is positive when it is on the OUTGOING side (by convention light comes from left)

m = y’/y = -s’/s

Chapter 25

Optical Instruments

The camera

• The shutter controls the exposure time and this depends on the film (which would be chemistry, the darkening of silver salts on exposure to light).

• The size of the opening provides interesting physics and is calibrated as “f-stops”. See page 838 in your text.

• The f-number = focal length/aperture diameter

f-number = f/D

The intensity is proportional to the square of the diameter

The projector

The position of the projector bulb, lens, and screen image actually serve as a “camera in reverse”

The eyeThe physics of eyeball optics and the chemistry of rhodopsin’s conformational changes to produce sight is a masterpiece of design and function.

Aging changes the focal point of an eye – Table 25.1

Hyperoptic correction

Myopic correction

• Lenses for correcting vision are described in terms of power which is defined as the inverse of the focal length expressed in meters:

The unit of this “power” is the DIOPTER

Correction for a farsighted person: use s=25 cmand a converging lens

Correction for a near-sighted person: use s=∞and a diverging lens

The magnifier

Angular Magnification M:M = θ’/θ M=25cm/f(cm)

The microscope

The microscope

Microscope

• m1= -s1’/s1

• M=m1M2 = (25cm)s1’/f1f2