Physics 222 Exam Review
Outline
ā¢ Overview/Mind-mapā¢ What each equation doesā¢ Practice Problems
Sorry about the boring theme.
ā¢ I couldnāt find a suitable theme that I liked, that didnāt mess up my text.
ā¢ However, looking at green is said to increase creativity and stimulate brain function. May use this later.
Useful tip: Storing variables in calculator
Charge
Electric Force
Electric Field
Potential EnergyElectric Potential
Divide by q
Multiply by q
Dipole
Interacts with dipole
Capacitors
Resistors
Overview
ā¢ Fluidsā¢ Electric force -> Electric fieldā¢ Potential energy -> Electric potentialā¢ E->V and V->Eā¢ Capacitors and energy stored inside themā¢ Resistors
š=š¹š“
ā¢ This is the definition of Pressure: Force/Area
š=š0+ššš¦ā¢ Used to calculate the pressure at a depth of y
in some medium, usually water.ā¢ Example: 5 m deep under the water, pressure=
šššš”
=š“š£=šššš š”ššš”
ā¢ This is the continuity equation for fluid flow.ā¢ In English, it means that the amount of stuff
going through a pipe is constant, so shrinking the pipe means that the water will go faster.
š+ššš¦+12šš£2=šššš š”ššš”
ā¢ Also known as Bernoulliās Equationā¢ Classic problem: calculating velocity of water
shooting out of a hole in a container.ā In the case that the radius of the hole is small, the
velocity at the bottom simplifies to where y is the distance from the water level to the hole.
Questions?
š š¶šš¢šššš=šš
š1š2š2
ļæ½Ģļæ½
š¬=šš0
ā¢ Just like electric force, but without the test charge q0. Itās still a vector.
š¬=šššš 2ļæ½Ģļæ½
ā¢ Electric field of a point charge.
Electric field lines go from + to -.
ā¢ Also, line density indicates field strength
š=ĀæšāØš ā¢ Dipole moment, BY DEFINITIONā¢ Notice: Dipole moment points from negative
to positiveā¦.opposite of the direction E points
š=šĆš¬ā¢ Torque on a dipole by the external electric
fieldā Note that E is not the E produced by the dipoleā E is external
ā¢ Torque is maximum when dipole moment and E are perpendicular.
š=āš ā š¬ā¢ Potential energy is minimum (also called stable
equilibrium) when two things are true:ā Dipole moment is parallel to Eā Dipole moment points in the same direction as E.
ā¢ Potential energy is maximum (also called unstable equilibrium) when two things are true:ā Dipole moment is parallel to E.ā Dipole moment points in the opposite direction as E.
Questions?
ā¢ Also known as Gaussās Lawā¢ Really there are two equations hereā¦but
theyāre both equally validā¦always.
Steps in solving Gaussās Law Problems
ā Draw a picture of the object. Pick a good Gaussian surface.
ā Write down the expression of Gaussās Law that involves the dot product between E and A. (If E is perpendicular to A, the flux is 0 for that surface. Otherwise, use symmetry to get rid of the integral.)
ā Write down the expression of Gaussās Law that involves the total charge q.
ā Set the two expressions equal to each other and eliminate variables.
šø=šš2šš
ļæ½Ģļæ½
ā¢ Electric field a distance r away from a long wire with charge density .
š¬=Ā±š2š
ļæ½Ģļæ½
ā¢ This one is especially important.ā¢ This is the electric field anywhere away from a
large sheet of charge.ā¢ Notice that the electric field doesnāt depend
on distance, and always points perpendicular to the surface.
ā¢ Classic problem: What is the electric field between two parallel plates of charge Q and area A?
ā¢ Answer: Since you have two plates of opposite charge, the E fields add, and thusā¦
ā¢
ā¢ These relations let you go from either E to V or vice-versa. If you know one, you can calculate the other.
š=ā Īš=āš0 ĪšThis equation can be used to:ā¢ If youāre given you can find the work done.ā¢ If a point charge of charge q0 goes through a
potential difference of it tells you the work done on the charge.
š=š0šā¢ This is the defining relation between potential
energy (U) and electric potential (V).ā¢ Note: since q0 can be positive or negative, U
and V do not necessarily have the same sign.ā¢ One more time: Electric potential (V) is not the
same thing as electric potential energy (U)ā¢ But letās rewrite it.
š=š /š0Similar to: .
š=šššš
ā¢ Electric potential of a point charge q, a distance r away, assuming V=0 at infinity.
ā¢ Potential goes up as you get closer to the point charge.
Īš=Ā±šøšā¢ Rather important: This is the potential
difference between two parallel conducting plates, otherwise known as a capacitor.
ā¢ What is E for a capacitor again?
š¶=šš
ā¢ Definition of capacitanceā¢ C=Charge Q/ Voltage drop
š¶=š0š“š
ā¢ Special case of capacitance when youāre looking at a parallel plate capacitor.
ā¢ Notice that the capacitance doesnāt depend on the charge on the plates.
š¶šš=š¶1+š¶2+ā¦ā¢ Adding capacitors in PARALLEL.
1š¶šš
=1š¶1
+1š¶2
+ā¦
ā¢ Adding capacitors in SERIES.
š¶=4 šš0šššāš
ā¢ Special case of capacitance when youāre looking at a two concentric spherical conducting shells.
ā¢ The radius of the smaller shell is a, the radius of the larger shell is b.
š¶=4 šš0š ā¢ The capacitance of a single spherical shell of
radius R
š=12š¶š 2= š2
2š¶=12šš
ā¢ You use these equations to calculate the stored energy in a capacitor
ā¢ Okay, but thereās 3 different equations, so which one is appropriate for my problem?ā If they just ask you to calculate U, use the one that
has variables you know.ā If they ask you what happens to U if you double the
charge, halve d, etcā¦ā¢ If the capacitors are stand-alone, use .ā¢ If the capacitors are connected to a voltage source, use
š=š š0ā¢ This relates the permittivity of free space to
the permittivity in a medium of dielectric constant .
š¶=š C0ā¢ Relates capacitance without a dielectric (C0) to
capacitance with a dielectric.
š¢=12ššø2
ā¢ The energy density when you have an electric field E in a medium of permittivity
ā¢ For example, letās say you have a cube (L=3) filled with water (. The cube has the same E field everywhere (E=5). ā Then u=ā Total stored energy=
š¼=šššš”
ā¢ Definition of current.
š=š¼š ā¢ Ohmās Law: A relationship between voltage,
current, and resistance.ā¢ Pretty fundamental.
š½=š¼š“
=ššš£š
ā¢ =Current densityā¢ n = density of charge carriersā¢ Vd=drift velocity (average velocity of charge
carriers)ā¢ q=charge on a charge carrier (usually e=
šø= š½ šā¢ Microscopic Ohmās Law:ā¢ E-field (E) = Current density (J) x resistivity (
š =ššæš“
ā¢ Resistance of a conductor of resistivity , length L, and cross-sectional area A
š=š0 (1+š¼ (š āš0 ) )ā¢ Resistivity changes as a function of
temperature.
š =š 0 (1+š¼ (š āš 0 ))ā¢ Resistance changes as a function of
temperature
š šš=š 1+š 2+ā¦ā¢ Adding resistances in series.
1š šš
=1š 1
+1š 2
+ā¦
ā¢ Adding resistances in parallel.
Practice Problems
In the figure to the right, there are two charges connected by a massless insulating rodā¦and remember to use VECTORS when appropriateā¦Draw the electric dipole.
Torque caused by the electric field=
Dipole moment=
Potential energy as it is right now=
Which way will the dipole begin to rotate? (Clockwise/Counter-clockwise)
How much work is done in rotating the dipole from its current position to the stable equilibrium position?
What does the work in question f?
A block of MagicFoam (length 10 cm, width 10 cm, height 3 cm) sits on top of a calm body of water. MagiFoam density=0.5 g/cm3. How much of the block is submerged?
A 10 kg block floats in the water. What is the buoyant force on it?
A house with a roof of area 5 m2 has winds of 50 m/s above it. What is the force on the roof caused by the pressure difference?
How much energy does it take to bring two electrons within .1 n of each other?
Some water is flowing at a rate of 20 mph in a pipe. Further on in the pipe, the pipe halves its diameter. What is the new speed of the water?
If current is going from your hand to your foot, which direction are
the electrons going?
Final Questions?
Thank you, and good luck!