PHYS 222 SI Exam Review3/31/2013
Answer: D
Answer: D,D
Answer: D,C
What to do to prepare
โข Review all clicker questions, but more importantly know WHY
โข Review quizzes
โข Make sure you know what all the equations do, and when to use them
SI Leader Secrets!Extra problems?
Visit the website below to get past exams all the way back to 2001!! (Note: the link below has stuff that you wouldnโt otherwise see)
http://course.physastro.iastate.edu/phys222/exams/ExamArchive222/exams/
๐ (๐ก )=๐ (โ )(1โ๐โ๐ก๐ )
โข These are all equations used for an RC circuit.
๐ (๐ก )=๐ (โ )(1โ๐โ๐ก๐ )
โข Used to find the charge Q on the capacitor in an RC circuit that initially has no charge and is slowly brought to a maximum charge .
โข What is
๐ (๐ก )=๐ (0 )๐โ ๐ก๐ ,๐ (0 )=๐ถ๐
โข Used to find the charge Q on the capacitor in an RC circuit that initially has charge Q(0) and has been disconnected from the power source.
โข I(t) is used to find the current in the resulting circuit. As before,
๐ญ=๐ (๐ฌ+๐ร๐ฉ)โข Used to find the force on a point charge of
charge q in an electric field E and magnetic field B.
โข Notice that the magnetic force is , and only exists if the charge is moving.
๐๐ญ=๐ผ ๐ ๐ร๐ฉโข This is the differential form of the magnetic
force on a length of wire carrying current.โข Probably more useful in this form:
โข Note that if the wire and B field are pointing in the same direction, the force is zero.
ฮฆ๐ต= โซ ๐ฉโ ๐ ๐จ is the magnetic flux through a closed surface.
Ex: A uniform B field of 5 T goes through a circular loop of wire of radius 10 m, What is the magnetic flux?Ans:
๐ =๐๐ฃ|๐|๐ต
โข Here, a charge of magnitude q and mass m is acted on by a constant B field. As a result, the charge moves in a circle of radius R and its tangential speed is v.
๐=๐ผ ๐จโข This is the equation for the magnetic dipole
( of a loop of current.โข is a vectorโข As an example,
if the radius is4 m and I=2,then up
๐=๐ร๐ฉโข This gives the torque on a magnetic dipole by
a magnetic field.โข Note that torque is zero if the magnetic dipole
and the B field point in the same direction.
๐=โ๐ โ ๐ฉโข This gives the potential energy of a magnetic
dipole in a magnetic field.
๐ฉ=๐04๐
๐ ๐ร ๏ฟฝฬ๏ฟฝ๐2
โข The equation for the magnetic field produced by a moving charge q at a speed v.
โข is just the distance away from the moving charge.
โข just means to use the right hand rule to determine which direction the magnetic field points.
๐ ๐ฉ=๐04๐
๐ผ ๐ ๐ร ๏ฟฝฬ๏ฟฝ๐ 2
โข Same equation as before, except that instead of a single point charge moving, we have a current I.
โข This equation is probably easier to use in its linear, non-differential form ,
โข just means to use the right hand rule to determine which direction the magnetic field points.
Right-hand rule
๐ฉ=๐0 ๐ผ2๐ r
โข This is the magnetic field a distance r away from an infinite straight wire carrying current I.
โข The direction of the field is given by the right hand rule.
๐น๐ฟ=
๐0 ๐ผ ๐ผ โฒ
2๐ ๐โข This gives the force between two parallel
wires. One wire carries current I, the other wire carries current Iโ.
โข If the currents are pointing in the same direction, the force is attractive. If they are opposite, the force is repulsive.
โข Is the force attractive or repulsive?โข Answer: attractive.
๐2= 1๐0๐0
โข I doubt youโd find a practical use for this equation in exam 2, because it really only says that the speed of light squared is equal to the inverse of the products of two constants. Cool, but not really something testable.
๐ต๐ฅ=๐0๐๐ผ ๐2
2 (๐ฅ2+๐2 )32
โข Letโs say you have a wire bent in a circle of radius a (in the picture itโs shown as R), with N turns. This equation gives the B field at the center of the circle a distance x above the center (if the circle is in the x-y plane, the variable x is the z coordinate).
โข The direction of the B field is given by the right hand rule, as discussed earlier.
๐ต๐ฅ=๐0๐๐ผ2๐
โข This equation is really just a special case of the previous one. This is the B field at the center of the circle, in the plane.
Question:
โข In the picture does the B field produced by the current point into the page or out of the page?
Question:
โข In the picture does the B field produced by the current point into the page or out of the page?
โข Answer: Into the page.
๐ต=๐0๐๐ผโข This is the equation for the field inside of a
solenoid.โข Note that it is a uniform field (i.e. everywhere
inside of the solenoid itโs the same).โข Lowercase n is the turns per length.
โฎ๐ฉ โ ๐ ๐=๐0 ๐ผ๐๐๐โข This is sometimes known as Ampereโs law.โข Can be used to derive many magnetic fields,
for example this one: . (Field away from any infinite straight wire)
๐=โ๐๐ฮฆ๐ต
๐๐กโข This equation is known by many names,
including Faradayโs Law and Lenzโs Law, depending on who you talk to.
โข Basically it says that a current loop without a voltage or current source can have an induced voltage if thereโs a changing magnetic flux inside the loop.
โข Note that the direction of the EMF is OPPOSITE the change in flux.
๐=โฎ (๐ร๐ฉ )โ ๐ ๐โข This is just another way of expressing the EMF.โข Recall is the magnetic force, so here weโre
sort of (thereโs no q up there) saying that the path integral of the magnetic force is equal to the emf.
โฎ๐ฌ โ ๐ ๐=โ ๐ฮฆ๐ต
๐๐กโข This just says that an induced E field is what
causes the induced EMF seen in the earlier equation:
โข Notice how thereโs an N missing in the equation up top. Thatโs because includes the N already, whereas in the bottom equation it doesnโt.
โฎ๐ฉ โ ๐ ๐=๐0 (๐๐ถ+ ๐๐ท )๐๐๐โข This is a copy of an equation we saw earlier,
except that it includes the displacement current.
โข What is the displacement current? The equation is on the next page, but the physical meaning is that itโs not a true current, but rather a mathematical construction to deal with changes in electric flux.
๐๐ท=๐๐ฮฆ๐ธ
๐๐กโข Hereโs the equation for displacement current.
โฎ๐ฌ โ ๐ ๐จ=๐๐๐๐
๐0โข One of the so-called โMaxwellโs Equationsโโข Also known as Gaussโs law.โข Used to calculate the E fields for many
common charge shapes, such as spheres and cylinders. (Theoretically can be used for complicated ones too, but that requires fancy mathematical software)
โฎ๐ฉ โ ๐ ๐จ=0โข One of the so-called โMaxwellโs Equationsโโข Says that the magnetic flux through a closed,
3-D surface is always zero.
โฎ๐ฌ โ ๐ ๐=โ ๐ฮฆ๐ต
๐๐กโข One of the so-called โMaxwellโs Equationsโโข This is basically the same as the induced EMF
equation.
โฎ๐ฉ โ ๐ ๐=๐0 (๐๐ถ+๐0๐ฮฆ๐ธ
๐๐ก )๐๐๐๐
โข One of the so-called โMaxwellโs Equationsโโข This equation basically appears twice on the
equation sheet.
๐1=โ๐๐๐2๐๐ก
โข If you have two loops of current with mutual inductance M, and a current i2 is going through one of them, then an emf (voltage) is produced through the other one, which excites a current in that one.
๐2=โ๐๐๐1๐๐ก
โข If you have two loops of current with mutual inductance M, and a current i1 is going through one of them, then an emf (voltage) is produced through the other one, which excites a current in that one.
โข Basically the same idea as the last equation.
๐=๐1ฮฆ๐ต 2
๐1=๐ 2ฮฆ๐ต 2
๐1โข The definition of mutual inductance M. Use the
side of the equation that is relevant.โข Note that although it appears that M depends
on current i, the fact of the matter is that M never depends on i because the i in the numerator cancels with the i in the denominator.
โข There is an i in the numerator because flux depends on B, and B depends on i.
๐=โ ๐ฟ ๐๐๐๐กโข This is the induced emf across an inductor.
Note that the induced emf occurs opposite the change in current.
๐ฟ=๐ฮฆ๐ต
๐โข Definition of self-inductance L.
๐=๐ผโ(1โ๐โ ๐ก๐ )
โข Current across an inductor in an LR circuit when you just start flowing current in the circuit.
๐=๐ผ 0๐โ ๐ก๐
โข Current across an inductor in an LR circuit when you just stop flowing current in the circuit.
๐= ๐ฟ๐
โข The time constant in LR circuits.
๐ฟ=๐0๐2๐ฟ ๐ดโข Self inductance of a solenoid of n turns per
length, of length L, and cross sectional area A.
๐=12 ๐ฟ๐ผ
2
โข Energy contained within an inductor (i.e. solenoid).
๐ข=๐ต22๐0
โข Energy density for a point with a magnetic field B.
โข Not really covered in lecture as far as I recall
โข The equation that tells you the charge q on a capacitor in an LC circuit.
โข Notice that itโs oscillatory- Simple Harmonic Motion!
โข The frequency depends on L and C
)
โข This is an RLC circuit.โข The idea is similar to the LC circuit, except that
now the charge q is also exponentially decreasing as it oscillates.
โข The oscillation frequency depends on L, C, and R.
Past exam problemsโฆ.
Answer: C
Answer: A
Answer: D
Answer: B
Answers: D, B
Answers: A,D
Answer: D
Answer: B, D
Answer: D
Answers: C, B
Answers: C, B
Answers: E, B
Answers: A,D
Answer: E
C, D, E
D, B
D, D
D
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