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 q 1 and q 2 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 |q 1 q 2 |/r 2

q1q1 q2q2 Additive forces q3q3 r 12 r 23 r 13

ELECTRIC FIELD

GAUSS’s LAW The total flux Φ E coming out of any closed surface is proportional to the total electric charge Q encl inside the volume surrounded by this surface. Φ E = Q encl / ɛ o Ɛ o = 8.854x C 2 /(N.m 2 )

Chapter 18 Electric Potential and Capacitance

ELECTRIC POTENTIAL ENERGY Electric 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 V ab between the conductors (plates): C =Q/V ab 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 = ɛ 0 A/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) U capacitor = (1/2) CV 2

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/I The 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 = V ab I The unit for power is the watt 1W = 1J/s

Power for a pure resistor: For a pure (single) resistor, we have: P=V ab I Since V= RI P = RI 2 or P = V 2 ab /R

Connections in series R eq = R 1 + R 2 + R 3 SAME CURRENT DIFFERENT POTENTIAL

Connections in parallel 1/R eq = 1/R 1 + 1/R 2 + 1/R 3 SAME POTENTIAL DIFFERENT CURRENT

Chapter 20

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 = mv 2 /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 = μ 0 I/(2πr) r is the distance from the wire μ 0 is called the permeability of vacuum μ 0 = 4π x 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 = μ 0 L(I 1 I 2 )/(2πr) Force per unit length F/L = μ 0 (I 1 I 2 )/(2πr)

Currents in a loop Magnetic field at the center of a circular loop B = μ o I /(2R) For N loops: B = μ o NI /(2R)

Magnetic field of a Solenoid: B = μ o nI n = number of turns per unit length n = N/L SOLENOID

Chapter 21 Electromagnetic Induction

Does the field induce a current or not?

Magnetic flux at various orientations

FRADAY’s LAW When the magnetic flux Φ B changes in time, there is a an induced emf directly proportional to the time rate of change of the magnetic flux : ɛ = |Δ Φ B /Δt | If we have a coil with N identical turns, then ɛ = N |Δ Φ B /Δt |

Lenz’s Law

Self-inductance

Transformers

TRANSFORMERS V 2 / V 1 = N 2 / N 1 If energy completely transformed V 1 I 1 = V 2 I 2

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 V R = RI

Resistance and Reactance – Figure 22.6

An Inductor in a circuit V L = X L I X L = ωL

An Inductor in a circuit

An Inductor in a circuit –

A capacitor in an AC circuit V C = X C I X C = 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

Power in AC Circuits

Chapter 23 Electromagnetic Waves

Electromagnetic waves

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 = 3.00x10 8 m/s Unlike other mechanical waves, there is no need for a medium to propagate.

v wave = λ /T v wave = λ f for light: c= λ f Speed of a wave

S = Ɛ 0 cE 2 S = EB/μ o S av = (1/2) Ɛ 0 cE 2 max S av = (E max B max )/(2μ 0 ) The INTESITY of the wave I : I = S av

Reflection and refraction

Refraction

Definition of Index of Refraction The index of refraction of an optical material is n = c/v Where 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 =λ 0 /n

Relation between angles The angle of reflection θ r is equal to the angle of incidence θ a for al wavelengths and pair of materials. For monochromatic light the angle of refraction θ b is related to the angle of incidence θ a by: n a sin θ a = n b sin θ b 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 Sinθ crit = n b /n a

Chapter 24 Geometric Optics

Reflections at a plane surface Review 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 reversal Have 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

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

Reflection and production of paraxial rays

Specific ray tracing for mirror analysis

A complete image construction

Refraction at spherical surfaces (n a /s) +(n b /s’) = (n b -n a )/R m = y’/y = -(n a s’)/(n b s)

THIN LENSES

The converging lens – Converging lens f > 0

The principal rays for thin lenses

The converging lens – Diverging lens f < 0

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/R 1 ) – (1/R 2 )] (1/f) = (n-1)[(1/R 1 ) – (1/R 2 )] 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 eye The 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 cm and 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

Microscope m 1 = -s 1 ’/s 1 M=m 1 M 2 = (25cm)s 1 ’/f 1 f 2