Units:

SI Prefixes:

Y Z E P T G M K h da d c m μ n P f a Z y1

024102

1

101

8

101

5

101

2

109

106

103

102

101

100

10-

1

10-2

10-3

10-

610-9

10-

12

10-

1510-

18

10-

21

10-

24

yotta

zetta

exa

peta

tera

giga

mega

kilo

hecto

deca

(unit)

deci

centi

milli

micro

nano

pico

femto

atto

zepto

yocto

SI Base Units:

SI symbol named measuresm meter lengthkg kilogram masss second timeA ampere electric currentK kelvin temperature

Derived SI Units:

SI symbol named measures equivalent base unit

other equivalence

rad radian angle m*m-1

Hz hertz frequency s-1

N newton force kg*m*s-2

Pa pascal pressure kg*m-1*s-2 N*m-2

J joule energy kg*m2*s−2 N*mW watt power kg*m2*s-3 J*s-1

C coulomb electric charge A*sV volt electric potential

differencekg*m2*s-3*A-1 J*C-1 OR W*A-1

F farad electric capacitance kg−1*m−2*s4*A2 C*V-1

Ω ohm electric resistance kg*m2*s−3*A−2 V*A-1

°C degree Celsius temperature relative to 273.15 K

K

Wb weber magnetic flux kg·m2·s−2·A−1 V*sT tesla magnetic flux

densitykg·s−2·A−1 Wb*m-2

H henry inductance kg·m2·s−2·A−2 Wb*A-1

Constants:

g = 9.8 [m/s, downward]

G = 6.67408 × 10-11 [m3/kg1*s2]

e = 1.6022 × 10-19 [C]

me = 9.11 × 10-31 [kg]

mn = 1.674929 x 10-27 [kg]

mp = 1.6726 × 10-27 [kg]

amu = 1.660540 x 10-27 [kg]

R = .08206 [L*atm/mol*K] = 8.314 [J/mol*K]

NA = 1 mol = 6.022E23

kB = R/NA = 1.381E-23 [J/K]

ε0 = 8.854 × 10-12 [F/m = A2*s4/kg*m3]

μ0 = 1.25663706 × 10-6 [m*kg*s-2*A-2]

k = 8.99 × 109 [N*m2*C-2]

Newtonian mechanics

Kinematics

∆ x⃗= v⃗0 t+12a⃗ t 2

∆ v⃗=a⃗ t

v f2−v i

2=2ax

Force and Impulse∑ F⃗=F⃗net=m a⃗F fric≤ μNF⃗ s=−k x⃗

p⃗=mv⃗J⃗=∆ p⃗=F⃗ ∆ t

Work and Energy

K=12

mv2

∆U g=mg∆ h

W=F∆r cosθ

U s=12k x2

Pavg=W∆t

P=Fv cosθ

Rotational Motion

ac=v2

r=ω2 r

x=θrv=ωra=αr

∆ θ⃗=ω⃗0t+12α⃗ t 2

∆ ω⃗= α⃗ t

ωf2−ωi

2=2αθ

K r=12

I ω2

L=Iωτ=Fr sinθ

Oscillations

x=xmax cos (ωt+φ)

T=2πω

T s=2 π √mk

T p=2π √ lg

T=1f

Gravitation

FG=−Gm1 m2

r2

UG=−Gm1 m2

r

Electricity & Magnetism:

Electrostatic Forces and Fields

F=k|q1||q2|

r 2 = 14 π ε0

|q1||q2|r2

E⃗= F⃗q0

V=k qr

∆V =−E∆ s

U E=qV=kq1 q2

r

φenclosed=qε0

φE=EA cosθ

Circuits

C= qV

=κ ε0 A

d

U c=12qV =1

2CV 2

I avg=∆q∆ t

V=IR

V=V 0sin 2πft=V 0 sinωt

V rms=V 0

√2

I=I 0sin 2 πft=I 0sin ωt

I rms=I 0

√2

P=IV

Pavg=12

I 0 V 0=I rmsV rms

R=ρ LA

C p=∑i

C i=C1+C 2+C3+…

1C s

=∑i

1C i

= 1C1

+ 1C2

+ 1C 3

+…

R s=∑i

Ri=R1+R2+R3+…

1R p

=∑i

1R i

= 1R1

+ 1R2

+ 1R2

+…

τ=RC

ω=2πf

XC=1

2 πfC

X L=2πfL

V rms=I rms Z

Z=√R2+ (X L−XC )2

f 0=1

2π √LC

Charging

q=q0(1−e−tRC )=q0(1−e

−tτ )

Discharging

q=q0 e−tRC=q0e

−tτ

Magnetism

FB=|q|vB sin θ

F c=m v2

r

FB=BIl sinθ

τ=NIABsin θ

magneticmoment=NIA

B=μ0

2πIr

Bsolinoid=μ0∋¿

φm=BA cosθ

ε avg=−N∆φm

∆t

ε=Blv

ε p

εs=

N p

N s

ε=ε 0sin ωt

ε 0=NABω

ε=−L ∆I∆ t

U L=12

L I 2

Erms=E0

√2

Brms=B0

√2

Energy density of magnetic field u= 12 μ0

B2

Energy density of electric field u=12

ε0 E2

Total energy density u=B2

μ0=ε E2

Waves & Optics:

S= PA

=uc

S=S0 cos2θ

v=fλ

n= cv

n1 sin θ1=n2sin θ2

θc=sin−1 n2

n1

d '=dn2

n1

sin θC=n2

n1

1d i

+ 1d0

=1f

M=hi

h0=

−d i

d0

f= R2

d sinθ=mλ

xm≈ mλLd

Atomic & Nuclear:

E=hf=pc

Kmax=hf −φ

λ= hp

E2=(mc2)2+( pc)2

Geometry & Trigonometry:

Rectangle

A=bh

Triangle

A=12

bh

Circle

A=π r2

C=2πr

Rectangular Prism

V=lwh

SA=2(lw+wh+hl)

Cylinder

V=π r2 l

SA=2πrl+2π r2

Sphere

V= 43

π r3

SA=4 π r2

Right triangle

a2+b2=c2

sin (θ )= oppositehypotenuse

cos (θ )= adjacenthypotenuse

tan (θ )= oppositeadjacent

College Physics II Final Review #1

1. Two charged particles are projected into a region where a magnetic field is directed perpendicular to their velocities. If the charges are deflected in opposite directions, what are the possible relative charges and directions?

a) zero net charge, opposite initial direction b) same charge, opposite initial direction c) same charge, same initial direction d) oppositely charged, opposite initial direction

2. What is another possible solution to the previous problem?

Oppositely charged, same direction

3. The net electric field is always __________ inside a conductor at equilibrium that is located inside of an external electric field.

a) Positiveb) negativec) zerod) infinity

4. What happens to the electric flux of a closed sphere surrounding some value of positive charge when the radius of the sphere is tripled.

a) The flux is increased by a magnitude of threeb) The flux is decreased by a magnitude of one thirdc) The flux is decreased by a magnitude of one ninthd) The flux stays the same

5. What is the time constant of an RL circuit?

a) R/Lb) LRc) L/Rd) NOTA

6. The drawing shows an equilateral triangle, each side of which has a length of 2.00 cm. Point charges are fixed to each corner, as shown. The 4.00 uC (micro-coulomb) charge experiences a net force due to the charges qA and qB. This net force points vertically downward and has a magnitude of 405 N. Determine the magnitudes and algebraic signs of the charges qA and qB.

qA = qB = -2.6 uC

7. An empty capacitor is connected to a battery and charged up. The capacitor is then disconnected from the battery, and a slab of dielectric material is inserted between the plates. Does the potential difference across the plates:

a) Increaseb) Remain the samec) Decrease

Because inserting the dielectric causes the capacitance C to increase. Since q = CV and q is fixed, the potential difference V across the plates must decrease in order for q to remain unchanged. The amount by which the potential difference decreases from the value initially established by the battery depends on the dielectric constant of the slab.

+4.00 uC

qA qB

8. A particle with a charge of -1.5 uC and a mass of 2.5 x 10^-6 kg is released from rest at point A and accelerates towards point B, arriving there with a speed of 42 m/s. The only force acting on the particle is the electric force. Which point is at the higher potential? Give your reasoning. What is the potential difference VB-VA between A and B?

VB>VAVB-VA = 1,470 V

9. The potential energy is characteristic of the charge-field system. The potential is characteristic of the field only. The potential has a value _______________ in an electric field.

a) Only at a point where there is a chargeb) At every point in an electric fieldc) At every point in space d) Only when we are looking

10. Point charges q and Q are positioned as shown. If q = +2.0nC, Q = -2.0nC, a = 3.0 m, and b = 4.0 m, what is the electric potential difference, VA - VB?

4.8 V

q

Q

a

a

A

B

b

11. Electric current is defined as the ____________, across a given area, per unit of _________.

a) Movement of charge; timeb) Movement of time; chargec) Flow of electric field; distanced) Flow of electric field; time

12. Two materials have different resistivities. Two wires of the same length are made, one from each of the materials. Is it possible for each wire to have the same resistance?

a) Yes, if the material with the greater resistivity is used for a thinner wire. b) Yes, if the material with the greater resistivity is used for a thicker wire.c) It is not possible

13. A stereo receiver applies a peak ac voltage of 34 V to a speaker. The speaker behaves approximately as if it had a resistance of 8.0 ohm. Determine the average power for this circuit.

a) 12 Wb) 69 Wc) 88 Wd) 72 W

14. Three resistors, 25, 45, and 75 ohm, are connected in series, and a 0.51 A current passes through them. What are the (a) the equivalent resistance and (b) the potential difference across the three resistors?

Req = 145 ohm, V25 = 12.75, V45 = 22.95, V75 = 38.25

15. Calculate the equivalent capacitance of four capacitors in series if the capacitors have values of 4 F, 3.5 F, 8 F, and 2 F.

Ceq = 0.86 F

16. A proton is projected with a velocity of 3.5 km/s into a magnetic field of 1.20 T perpendicular to the motion of the proton. What is the force that acts on the proton?

a) 13x10-16 Nb) 6.7x10-16 Nc) 0 Nd) 3.4x10-16 N

17. An electron moving perpendicular to a magnetic field of 3.7×10-2 T moves in a circle of radius 0.50cm. How fast is this electron moving?

a) 32.5 Mm/sb) 3.25 Mm/sc) 0.89 Mm/sd) 8.9 Mm/s

18. A rectangular loop of wire carrying a 4.0-A current and with certain dimensions is placed in a magnetic field of 0.60 T. The magnitude of the torque acting on this wire when its normal line makes a 60º angle with the magnetic field is 1.1 N· m. What is the area of this loop?

a) 0.26 m²b) 0.53 m²c) 0.40 m²d) 0.80 m²

19. A loose spiral spring carrying no current is hung from a ceiling. When a switch is thrown so that a current exists in the spring, how do the coils move?

a) closer together b) farther apart c) not at all d) widening the loop diameter

20. A wire carrying a 4 A current is placed at an angle of 60º with the respect to a magnetic field of strength 0.2 T. If the length of the wire is 0.6 m what is the magnitude of the magnetic force acting on the wire?

a) 0.4 Nb) 0.6 Nc) 0.8 Nd) 0.2 N

21. If the current in a wire is quadrupled, by what factor will the magnetic field distance r away change?

a) increase by a factor of 2b) increase by a factor of 4c) decrease by a factor of 4d) increase by a factor of 16e) remain unchanged

22. If the power over a solenoid is tripled, by what factor does the magnetic field generated increase?

a) B = √3· Bo

b) B = 1· Bo

c) B = 9· Bo

d) B = 3· Bo

23. If the number of turns in a rectangular coil of wire that is rotating in a magnetic field is halved, what happens to the induced emf, assuming other things constant?

a) It is doubled. b) It stays the same. c) It is reduced by a factor of 2. d) It is quadrupled.

24. A rectangular coil lies flat on a horizontal surface. A bar magnet is held above the center of the coil with its north pole pointing down. If the magnet is pulled away from the loop, what is the direction of the induced current in the coil if looking from above?

a) counterclockwise b) clockwise c) No current in the coil d) None of previous is correct

25. A conducting loop of wire has an area of 150 cm^2 and a resistance of 12.5Ω . There is a magnetic field of 100 T perpendicular to the loop. At what rate must this field be reduced to induce a current of 0.100 A in the loop?

a) 30.0 T/s b) 0.177 T/s c) 83.3 T/s d) 60.0 T/s

26. A circular loop of wire is held in a uniform magnetic field, with the plane of the loop perpendicular to the field lines. Which of the following will not cause a current to be induced in the loop?

a) keeping the orientation of the loop fixed and moving it along the field lines b) rotating the loop about an axis perpendicular to the field lines c) pulling the loop out of the field d) crushing the loop

27. At an instant of time during the oscillations of an LC circuit, the charge is momentarily maximum. At this instant, the energy stored across the inductor is described by which of the following?

a) different from that across the capacitor b) has its maximum value c) is impossible to determine d) zero

28. At an instant of time during the oscillations of an LC circuit, the current is momentarily zero. At this instant, the voltage across the capacitor is described by which of the following?

a) different from that across the inductor b) has its maximum value c) is impossible to determine d) zero

29. Light rays from an object travel through a pinhole. The rays reach the other side and form what type of image?

a) Upright, Realb) Inverted, Realc) Upright, Virtuald) Inverted, Virtuale) No image formed

30. In a young’s double slit experiment, the angle between the central bright fringe and the fourth bright fringe is 7 degrees. What is the distance between the two slits if the frequency of light is 5.4x10^14 Hz?

a) 1.2 x 10-5 mb) 0.1 x 10-5 mc) 1.8 x 10-5 md) 7.0 x 10-5 m

31. What happens to the wavelength light as it changes mediums from air to glass?

a) Increase in wavelengthb) Decrease in wavelengthc) Nothing happensd) Everything happens

32. A laser is fired directly into a tank. If the laser travels 30 cm inside the tank and is filled with an oil that has a refractive index of n = 2.5, then how many wavelengths of the violet laser (lamda = 400 nm) fits inside of the tank?

a) 1.88 x 106

b) 8.22 x 106

c) 2.00 x 106

d) 1.41 x 106

33. Which of the following statements is always true?

a) Current is the flow of electrons.b) The fundamental unit of charge is 1 Coloumb.c) The rate which you change magnetic flux in a closed loop is inversely

proportional to induced emf.d) The net electric field inside of a conductor is zero.

34. If the sun was twice as hot and just as big, by what factor would the radiant intensity change on the surface of earth?

a) Increase by a factor of 2b) Increase by a factor of 4c) Increase by a factor of 8d) Increase by a factor of 16e) Would not change

Remember to study other material in addition to this review. I have received no assistance from the teacher in making this guide.