PHYS 222 SI Exam Review3/31/2013

Answer: D

Answer: D,D

Answer: D,C

What to do to prepare

• Review all clicker questions, but more importantly know WHY

• Review quizzes

• 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 wouldn’t otherwise see)

http://course.physastro.iastate.edu/phys222/exams/ExamArchive222/exams/

𝑄 (𝑡 )=𝑄 (∞ )(1−𝑒−𝑡𝜏 )

• These are all equations used for an RC circuit.

𝑄 (𝑡 )=𝑄 (∞ )(1−𝑒−𝑡𝜏 )

• 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 .

• What is

𝑄 (𝑡 )=𝑄 (0 )𝑒− 𝑡𝜏 ,𝑄 (0 )=𝐶𝑉

• 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.

• I(t) is used to find the current in the resulting circuit. As before,

𝑭=𝑞 (𝑬+𝒗×𝑩)• Used to find the force on a point charge of

charge q in an electric field E and magnetic field B.

• Notice that the magnetic force is , and only exists if the charge is moving.

𝑑𝑭=𝐼 𝒅𝒍×𝑩• This is the differential form of the magnetic

force on a length of wire carrying current.• Probably more useful in this form:

• Note that if the wire and B field are pointing in the same direction, the force is zero.

Φ𝐵= ∫ 𝑩⋅𝒅𝑨 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:

𝑅=𝑚𝑣|𝑞|𝐵

• 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.

𝝁=𝐼 𝑨• This is the equation for the magnetic dipole

( of a loop of current.• is a vector• As an example,

if the radius is4 m and I=2,then up

𝝉=𝝁×𝑩• This gives the torque on a magnetic dipole by

a magnetic field.• Note that torque is zero if the magnetic dipole

and the B field point in the same direction.

𝑈=−𝝁 ⋅𝑩• This gives the potential energy of a magnetic

dipole in a magnetic field.

𝑩=𝜇04𝜋

𝑞 𝒗× �̂�𝑟2

• The equation for the magnetic field produced by a moving charge q at a speed v.

• is just the distance away from the moving charge.

• just means to use the right hand rule to determine which direction the magnetic field points.

𝒅𝑩=𝜇04𝜋

𝐼 𝒅𝒍× �̂�𝑟 2

• Same equation as before, except that instead of a single point charge moving, we have a current I.

• This equation is probably easier to use in its linear, non-differential form ,

• just means to use the right hand rule to determine which direction the magnetic field points.

Right-hand rule

𝑩=𝜇0 𝐼2𝜋 r

• This is the magnetic field a distance r away from an infinite straight wire carrying current I.

• The direction of the field is given by the right hand rule.

𝐹𝐿=

𝜇0 𝐼 𝐼 ′

2𝜋 𝑟• This gives the force between two parallel

wires. One wire carries current I, the other wire carries current I’.

• If the currents are pointing in the same direction, the force is attractive. If they are opposite, the force is repulsive.

• Is the force attractive or repulsive?• Answer: attractive.

𝑐2= 1𝜇0𝜖0

• I doubt you’d 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.

𝐵𝑥=𝜇0𝑁𝐼 𝑎2

2 (𝑥2+𝑎2 )32

• Let’s say you have a wire bent in a circle of radius a (in the picture it’s 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).

• The direction of the B field is given by the right hand rule, as discussed earlier.

𝐵𝑥=𝜇0𝑁𝐼2𝑎

• 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:

• In the picture does the B field produced by the current point into the page or out of the page?

Question:

• In the picture does the B field produced by the current point into the page or out of the page?

• Answer: Into the page.

𝐵=𝜇0𝑛𝐼• This is the equation for the field inside of a

solenoid.• Note that it is a uniform field (i.e. everywhere

inside of the solenoid it’s the same).• Lowercase n is the turns per length.

∮𝑩 ⋅𝒅𝒍=𝜇0 𝐼𝒆𝒏𝒄• This is sometimes known as Ampere’s law.• Can be used to derive many magnetic fields,

for example this one: . (Field away from any infinite straight wire)

𝜖=−𝑁𝑑Φ𝐵

𝑑𝑡• This equation is known by many names,

including Faraday’s Law and Lenz’s Law, depending on who you talk to.

• Basically it says that a current loop without a voltage or current source can have an induced voltage if there’s a changing magnetic flux inside the loop.

• Note that the direction of the EMF is OPPOSITE the change in flux.

𝜖=∮ (𝒗×𝑩 )⋅𝒅𝒍• This is just another way of expressing the EMF.• Recall is the magnetic force, so here we’re

sort of (there’s no q up there) saying that the path integral of the magnetic force is equal to the emf.

∮𝑬 ⋅𝒅𝒍=− 𝑑Φ𝐵

𝑑𝑡• This just says that an induced E field is what

causes the induced EMF seen in the earlier equation:

• Notice how there’s an N missing in the equation up top. That’s because includes the N already, whereas in the bottom equation it doesn’t.

∮𝑩 ⋅𝒅𝒍=𝜇0 (𝑖𝐶+ 𝑖𝐷 )𝑒𝑛𝑐• This is a copy of an equation we saw earlier,

except that it includes the displacement current.

• What is the displacement current? The equation is on the next page, but the physical meaning is that it’s not a true current, but rather a mathematical construction to deal with changes in electric flux.

𝑖𝐷=𝜖𝑑Φ𝐸

𝑑𝑡• Here’s the equation for displacement current.

∮𝑬 ⋅𝒅𝑨=𝑄𝑒𝑛𝑐

𝜖0• One of the so-called “Maxwell’s Equations”• Also known as Gauss’s law.• 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)

∮𝑩 ⋅𝒅𝑨=0• One of the so-called “Maxwell’s Equations”• Says that the magnetic flux through a closed,

3-D surface is always zero.

∮𝑬 ⋅𝒅𝒍=− 𝑑Φ𝐵

𝑑𝑡• One of the so-called “Maxwell’s Equations”• This is basically the same as the induced EMF

equation.

∮𝑩 ⋅𝒅𝒍=𝜇0 (𝑖𝐶+𝜖0𝑑Φ𝐸

𝑑𝑡 )𝑒𝑛𝑐𝑙

• One of the so-called “Maxwell’s Equations”• This equation basically appears twice on the

equation sheet.

𝜖1=−𝑀𝑑𝑖2𝑑𝑡

• 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.

𝜖2=−𝑀𝑑𝑖1𝑑𝑡

• 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.

• Basically the same idea as the last equation.

𝑀=𝑁1Φ𝐵 2

𝑖1=𝑁 2Φ𝐵 2

𝑖1• The definition of mutual inductance M. Use the

side of the equation that is relevant.• 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.

• There is an i in the numerator because flux depends on B, and B depends on i.

𝜖=− 𝐿 𝑑𝑖𝑑𝑡• This is the induced emf across an inductor.

Note that the induced emf occurs opposite the change in current.

𝐿=𝑁Φ𝐵

𝑖• Definition of self-inductance L.

𝑖=𝐼∞(1−𝑒− 𝑡𝜏 )

• Current across an inductor in an LR circuit when you just start flowing current in the circuit.

𝑖=𝐼 0𝑒− 𝑡𝜏

• Current across an inductor in an LR circuit when you just stop flowing current in the circuit.

𝜏= 𝐿𝑅

• The time constant in LR circuits.

𝐿=𝜇0𝑛2𝐿 𝐴• Self inductance of a solenoid of n turns per

length, of length L, and cross sectional area A.

𝑈=12 𝐿𝐼

2

• Energy contained within an inductor (i.e. solenoid).

𝑢=𝐵22𝜇0

• Energy density for a point with a magnetic field B.

• Not really covered in lecture as far as I recall

• The equation that tells you the charge q on a capacitor in an LC circuit.

• Notice that it’s oscillatory- Simple Harmonic Motion!

• The frequency depends on L and C

)

• This is an RLC circuit.• The idea is similar to the LC circuit, except that

now the charge q is also exponentially decreasing as it oscillates.

• The oscillation frequency depends on L, C, and R.

Past exam problems….

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