Exam 1 S16 Phys 1220 3/3/2016

__________

name

Each of problems 1 to 7 is of equal value.

You can skip two problems. You cannot skip both, problem 1 and problem 4. If you work all problems, we will count the best grades according to the above rules.

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. In some cases a large part of the points may be reserved for the ‘easy’ parts. Do not skip the answers to those parts!

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 final 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.

All multiple choice questions may have more than one correct answer. For full credit, you need to mark all correct answers and mark no incorrect answer.

1. Electrostatics: Gauss’s Law

Consider two concentric, conducting shells. The inner shell has an inner and

outer radius of 2.5 R

4∧3 R

4 and the outer shell has an inner and outer radius of

5 R4

∧6 R

4. The inner shell carries a charge of -2q, the outer shell carries a charge of

-2q.

a) Draw the E(R) graph.b) Draw the V(R) graph.

Include in your drawing exact expressions for the steepness of the curves in terms of q and R and exact E and V values in terms of q and R on the vertical axis for each of the radii where charge resides.

2. Circuitry: Resistor Networks

Consider the circuit shown below.

a) Derive the general resistor network rules for series and parallel networks:

b) Calculate the equivalent resistance of the circuit.

c) Find the current through the 2 resistor. Explain!

d) What is the voltage drop across the 6 resistor closest to the source? Explain!

3. Electrostatics: Lecture video discussion

Recall the lecture videos on demonstrating how charges accumulate on conductors.

a) Describe an experimental setup that would demonstrate this principle. You can either choose the setup that was shown in the lecture video or you can design your own setup.

b) Name two likely experimental errors that might skew the results, assuming that great care was taken to set the experiment up properly. Explain what each error would do to the data.

c) Why is it important to make independent repetitions in lab and what exactly does it entail to make independent repetitions? What happens to the data when you fail to make independent repetitions?

4. Electrostatics: Gauss’s Law

An insulating spherical shell of inner radius R and outer radius 1.5R is charged with -2q. Apply Gauss's Law and find a formula for the electric field inside and outside of the shell.

a) Divide into suitable regions. Explain your Gaussian surfaces and explain which part of the field due produces flux and which part does not.

b) Determine the enclosed charge as function of distance, r.

c) Calculate the formulas for E in the regions. Do not forget that there are some regions with easy answers.

5. Electrostatics: Point Charges

Consider two point charges which are 4[cm] apart. q1 = + 4[nC] and q2 = + 2[nC].

a) Along the line that connects the two charges, where is the electric field due to both charges zero?

b) What is the potential difference due to the two charges at two points above the axis which connects the charges?

The points are (1) 5 [cm] away from q1 and 9[cm] from q2 and (2) 9 [cm] away from q1 and 5[cm] from q2.

c) How much work does it cost to move a -1[nC] point charge between these two points?

6. Electrostatics: Point Charges

Three point charges with charge +2q, +4q, and -2q are arranged around point P as shown in the figure.

Hint: express your answer in multiples of ; b), c): find the lengths of the vectors and the angles at which the vectors point relative to the +x-axis

a) Sketch the three electric field vectors due to the three charges at point P. Sketch also the net field vector at the same point. Make sure all vectors are qualitatively correct (relative length and direction)

b) Determine the magnitude and direction of the net electric field at P due to all three charges.

c) Determine the magnitude and direction of the electrostatic force that the charge

-2q experiences due to the other two charges.

7. Five Short and Sweet Problems: answer any four

draw graphs, choose multiple choice answers, or write one line answers where appropriate

1- A spherically symmetric charge distribution has a charge density given as follows:

ρ (r )= ρ0∙(r2+ 2 rR

−2) for r ≤R

= 0 for r > R

where ρ0>0

Draw the charge distribution as function of r between r = 0 and r = R.

2- In the figure below four light bulbs are shown as resistors. The bulb that is labeled as ‘3’ has resistance 2R. The other bulbs all have the same resistance, R. The source has 110 [V].

Which statements about the situation are true? Mark each statement as T for true or F for false.

A- Bulb ‘1’ and ‘2’ shine with the same brightness when switch ‘S’ is open.

B- Bulb ‘2’ and ‘4’ experience the same potential difference when ‘S’ is open.

C- When ‘S’ is open the equivalent resistance is 1.5 R.

D- When switch ‘S’ is closed bulbs ‘1’, ‘2’, and ‘4’ get darker.

3- Starting from the definition of resistivity, derive the general expression for resistance.

4- Show why any spherical charge distribution looks from the outside like a point charge at its center.

5- Explain how the choice of a Gaussian Surface can simplify ∮ E ⋅d A .

Master Equations – Physics 1220

F= 14 π ε0

∙|q1|∙|q2|

r2 ∧E=F0

q0

ΦE=∫ E ∙d A=Qencl .

ε0

U= 14 π ε0

q0∑i

q i

ri∧V=U

q0∧E=−(i ∂V

∂x+ j ∂V

∂ y+ k ∂V

∂ z ) V=∫ E ∙ dl

I=dQdt

=n|q|vd A∧J=nq vd

ρ=EJ∧V =IRwith R=ρ L

A

P=V ab ∙ I=I2 R=V ab

2

R

Req=∑i

Ri (series ) 1Req

=∑i

1R i

(¿)

Kirchhoff Rules∑ I=0 ( junctionrule ) ,∑ V=0 (looprule)

Master Equations Phys 1210

Newton’s Laws

Σ F=0 ,Σ F=ma , F A→B=−FB →Afind the related component equations by replacing all relevant properties by their component values

Energy

W=F ∙ sK=12mv2U grav=mghU el=

12kx2

energy conservation E1=E2, E=∆ K+∆U+W other

Need to take your mind off the exam for a minute? Check these out:

Q: How many physicists does it take to change a light bulb?A: If the light bulb is a perfect sphere, one. The solution for a light bulb of arbitrary shape is left as an exercise to the reader.

Q: How many experimental physicists does it take to change a light bulb?A: They don't replace the bulbs, they repair them.

Q: How many theoretical physicists does it take to screw in a light bulb?A: Hmmmm, let's seeQ: That's correct!

"There are two possible outcomes: if the result confirms the hypothesis, then you've made a measurement. If the result is contrary to the hypothesis, then you've made a discovery." — Enrico Fermi (1901—1954), Italian physicist.

"There's a common myth that evidence speaks for itself. It doesn't. It just sits there on the lab table, incapable of speaking." "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." — Harlow Shapley (1885—1972).

"Discovery consists of seeing what everybody has seen and thinking what nobody has thought." — Albert Szent-Györgyi (1893-92), Hungarian-born US biochemist.

"There is no expedient to which a man will not resort to avoid the real labor of thinking."

"The trouble with the world is that the stupid are cocksure and the intelligent full of doubt." — Bertrand Russel.

The Feynman Problem Solving Algorithm:

1) Write down the problem. 2) Think very hard. 3) Write down the solution.