Download Training Exam based on S13 Phys 1220 ______ name

Training Exam based on S13 Phys 1220
__________
name
Each problem is of equal value.
You can skip two problems according to the following rules:
You can skip one of problems 1, 2, and 3.
You can skip one of problems 4, 5, 6, and 7.
If you work more than 5 problems, we will grade all and count the best results
consistent with the above rules. Make sure you work first all required problems
before you start to work extra problems!
Tips for better exam grades:
Read all problems right away and ask questions as early as possible.
Make sure that you give at least a basic relevant equation or figure for each
sub-problem.
Make use of the entire exam time.
Show your work for full credit. The answer ‘42’ only earns you any credit IF
‘42’ is the right answer. We reserve points for ‘steps in between’, figures,
units, etc. If all you give us is a numeric answer you may receive only a C
grade for the problem and in some cases even less.
No credit given for illegible handwriting or flawed logic in an argument.
1. Kirchhoff Rules
Use Kirchhoff rules to find your answers:
a) Draw a circuit for charging a capacitor that pertains to the situation of the
solution given in part c):
b) Derive the differential equations for charge and current as a function of time.
𝑡
c) The solution to the equation in part b) is 𝑞 = 𝐶 ∙ 𝜀 ∙ (1 − 𝑒 −𝑅𝐶 )
Consider the following circuit where both capacitors initially uncharged.
They will be charged by a 45[V] source when switch S is closed. How long
after closing will the potential have increased to 20[V]?
Figure 1
2. Kirchhoff Rules
A- Use the Kirchhoff rules to find the current through the battery and each
resistor in the circuit in figure 2.
B- What is the equivalent resistance of the network?
n/b: Full credit is only given, if you use Kirchhoff rules to find the results.
Figure 2
1.
3. Capacitor networks
Five plate capacitors are wired up in a network (see figure).
(all values in figure are in Farad)
a) Find the equivalent capacitance of the network.
b) For Vab = 20[V], how much charge is on each capacitor?
c)
How much energy is stored in the 1[F] capacitor?
d) If one doubles the distance between the plates of each capacitor, how
much energy is now stored in the network?
4. Magnetism: Force due to Moving Point Charges
Each of the lettered points at the corners of the cube represents a positive charge
q moving with a velocity of magnitude v in the direction indicated. The whole
region is in a uniform magnetic field, B, parallel to the -y –axis.
A- What is the direction of the resulting forces on each charge due to B?
B- In addition to the forces due to field B, each charge exerts an electrostatic and
a magnetic force on each other charge. What is the directions the magnetic force
of charge c on charge d and of charge e on charge c?
Figure 3
5. Magnetic Field due to Current Carrying Straight Wires
a) Rank the net magnetic field strength, Bnet , which each wire experiences.
b) Calculate the net magnetic force on the wire in the middle.
Show your work for full credit.
Figure 4
6. Magnetostatics
Three straight wires carry currents as shown in the figure below. Two wires are
parallel to each other and the third wire is perpendicular to both other wires.
Hint: Treat the wires as infinitely long.
Figure 5
a) Points P1 and P2 are 2[cm] away from the closest point on each of the
three wires. What is the net magnetic field at P1 and at P2?
b) Consider the 2[cm] long segment ‘a’ of the wire that carries -2I. Assume
that ‘a’ is sufficiently far from the region where all three wires come
together so that any effect due to the presence of the wire that carries ‘I’
can be neglected.
What is the force on the wire that carries +2I due to segment ‘a’? Is the
force attractive or repulsive?
7. Magnetic Fields and Magnetic Forces
Which of the following statements about uniform and non-uniform magnetic
fields are true?
For full credit, mark all true statements and none of the false statements and
explain briefly your reasoning in the space below each statement.
A) The net force on a current loop in a non-uniform magnetic field is zero.
B) The net force on a current loop in a uniform magnetic field is zero.
C) Moving electric charges produce magnetic fields in their neighborhood.
D) Moving electric charges produce uniform magnetic fields.
E) Current carrying wires produce magnetic fields in their neighborhood,
which point radially away from the wire.
F) Current carrying wires produce magnetic fields in their neighborhood and
the resulting field vector B at some point P is perpendicular to the distance
vector r between the field causing wire element dl and the point P.
Master Equations Phys 1220
1
𝐹=
∙
4𝜋𝜀0
|𝑞1 |∙|𝑞2 |
1
4𝜋𝜀0
𝐶 ≡
𝑄
𝑉𝑎𝑏
𝑈=
𝑄2
2𝐶
𝐼=
𝜌=
𝑑𝑄
𝑑𝑡
∑i
=
qi
ri
and V =
𝐶 𝑉2 =
𝑞0

𝜀0
𝑎𝑛𝑑 𝐶𝑝𝑙𝑎𝑡𝑒 = 𝜀0
1
2
𝐹0
𝑄𝑒𝑛𝑐𝑙.
 Φ𝐸 = ∫ 𝐸⃗ ∙ 𝑑𝐴 =
𝑈=
𝑎𝑛𝑑 𝐸⃗ =
𝑟2
1
2
U
q0
𝑎𝑛𝑑 𝐸⃗ = − (𝑖̂
𝐴
𝑑
𝑎𝑛𝑑, 𝑖𝑛 𝑠𝑒𝑟𝑖𝑒𝑠,
𝑄 𝑉 𝑎𝑛𝑑 𝑢 =
1
2
𝜕𝑉
𝜕𝑥
+ 𝑗̂
1
𝐶𝑒𝑞
𝜕𝑉
𝜕𝑦
+ 𝑘̂
𝜕𝑉
)
𝜕𝑧
1
= ∑𝑖 𝐶 , 𝑎𝑛𝑑, 𝑖𝑛 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙, 𝐶𝑒𝑞 = ∑𝑖 𝐶𝑖
𝑖
𝜀 𝐸2
= 𝑛 |𝑞| 𝑣𝑑 𝐴 𝑎𝑛𝑑 𝐽 = 𝑛 𝑞 𝑣𝑑
𝐸
𝐽
𝑎𝑛𝑑 𝑉 = 𝐼𝑅 𝑤𝑖𝑡ℎ 𝑅 = 𝜌
𝑃 = 𝑉𝑎𝑏 ∙ 𝐼 = 𝐼 2 𝑅 =
𝑅𝑒𝑞 = ∑𝑖 𝑅𝑖 (𝑠𝑒𝑟𝑖𝑒𝑠)
𝐿
𝐴
2
𝑉𝑎𝑏
𝑅
1
𝑅𝑒𝑞
1
= ∑𝑖 𝑅 (𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙)
𝑖
𝐾𝑖𝑟𝑐ℎℎ𝑜𝑓𝑓 𝑅𝑢𝑙𝑒𝑠 ∑ 𝐼 = 0 (𝑗𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑟𝑢𝑙𝑒), ∑ 𝑉 = 0 (𝑙𝑜𝑜𝑝 𝑟𝑢𝑙𝑒)
𝑡
𝜀
𝑡
Capacitor charging 𝑞 = 𝑄𝑓 ∙ (1 − 𝑒 −𝑅𝐶 ) 𝑎𝑛𝑑 𝑖 = 𝑅 ∙ 𝑒 −𝑅𝐶
⃗ and Φ𝐵 = ∮ 𝐵
⃗ ∙ 𝑑𝐴 = 0 and 𝐹 = 𝐼 𝑙 × 𝐵
⃗ (𝑓𝑜𝑟 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑤𝑖𝑟𝑒𝑠)
𝐹 = 𝑞𝑣 × 𝐵
⃗ = 𝜇0 ∙ 𝑞𝑣⃗×𝑟
𝐵
𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑓𝑖𝑒𝑙𝑑 𝑐𝑟𝑒𝑎𝑡𝑒𝑑 𝑏𝑦 𝑚𝑜𝑣𝑖𝑛𝑔 𝑐ℎ𝑎𝑟𝑔𝑒
4𝜋
𝑟2
⃗ =
𝐵
𝜇0
4𝜋
𝐵=
𝜇0 𝐼
2𝜋𝑟
∙
𝐼 𝑑𝑙 ×𝑟
𝑟2
𝐵𝑖𝑜𝑡 − 𝑆𝑎𝑣𝑎𝑟𝑡 𝑓𝑖𝑒𝑙𝑑 𝑐𝑟𝑒𝑎𝑡𝑒𝑑 𝑏𝑦 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑤𝑖𝑟𝑒 𝑐𝑎𝑟𝑟𝑦𝑖𝑛𝑔 𝑐𝑢𝑟𝑟𝑒𝑛𝑡
near a long straight wire and
𝐹
𝐿
=
𝜇0 𝐼∙𝐼′
2𝜋𝑟
𝑓𝑜𝑟 2 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑤𝑖𝑟𝑒𝑠
Need to put your mind off the test for a minute? Check this out:
A priest, a doctor, and an engineer were waiting one morning for a particularly slow group of
golfers.
Engineer: What's with these guys? We must have been waiting for 15 minutes!
Doctor: I don't know but I've never seen such ineptitude!
Priest: Hey, here comes the greenskeeper. Let's have a word with him.
Priest: Hi George. Say George, what's with that group ahead of us? They're rather slow aren't they?
George: Oh yes. That's a group of blind fire fighters. They lost their sight while saving our club house last
year. So we let them play here anytime free of charge!
(silence) Priest: That's so sad. I think I will say a special prayer for them tonight.
Doctor: Good idea. And I'm going to contact my ophthalmologist buddy and see if there's anything he can
do for them.
Engineer: Why can't these guys play at night?
Freshmen vs seniors:
Freshman: Reads the syllabus to find out what classes he can cut.
Senior: Reads the syllabus to find out what classes he needs to attend.
Freshman: Memorizes the course material to get a good grade.
Senior: Memorizes the professor's habits to get a good grade.
Freshman: Shows up at a morning exam clean, perky, and fed.
Senior: Shows up at a morning exam in sweats with a cap on and a box of pop
tarts in hand.
"A physicist is someone who averages the first 3 terms of a divergent series..."
"The good Christian should beware of mathematicians and all those who make empty prophecies. The
danger already exists that mathematicians have made a covenant with the devil to darken the spirit and
confine man in the bonds of Hell." — Saint Augustine.
"An approximate answer to the right problem is worth a good deal more than an exact answer to
an approximate problem."
"A hypothesis or theory is clear, decisive, and positive, but it is believed by no one but the man who
created it. Experimental findings, on the other hand, are messy, inexact things, which are believed by
everyone except the man who did that work."
"In theory there is no difference between theory and practice, but in practice there is."