Physics 212 – Midterm Exam II                                   NAME:______________________

Summer 2003                                                               STUDENT ID#:_______________

Prof. Milos Steinhart

 

INSTRUCTIONS: This is a closed book exam. You must show all of your work in the space provided for each question and you must include appropriate units and significant figures. If you need more space, use the other side of the paper but mark clearly to which problem and which question is your work related. Try to make your work as clear and transparent as you can. Even if you understand the problem well, think twice, what you are precisely asked.

Do not use other papers!

You are bound by the University’s Honor Code. Any evidence of cheating must be reported to the College of Arts and Sciences.

 

 

 

 

PLEASE CIRCLE ALL ANSWERS

All problems are worth 20 points.

 

 

 

 

 

 

 

 

SCORE

                                                           

                                                            Problem 1 _____________________

 

                                                            Problem 2 _____________________

 

                                                            Problem 3 _____________________

 

                                                            Problem 4 _____________________

 

                                                            Problem 5 _____________________

 

                                                            TOTAL    _____________________

Problem 1: A galvanometer has an internal resistance of Rg = 30 W and deflects full scale for an If = 50 mA current. Its accuracy is 1%. Make drawings and describe how to use this galvanometer to make:

 

a) (10) An ammeter to read currents up to Ia = 30 A ?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b) (10) A voltmeter to give a full-scale deflection of Vv = 1000 V ?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Problem 2: A coaxial cable consists of a solid inner conductor of radius R1, surrounded by a concentric cylindrical tube of inner radius R2 and outer radius R3. The conductors carry equal and opposite currents I0 distributed uniformly across their cross-sections.

Determine magnetic field at a distance r from the axis for:

 

a) (5) r < R1

 

 

 

 

 

 

 

 

 

 

b) (5) R1 < r < R2

 

 

 

 

 

 

 

 

 

 

c) (5) R2 < r < R3

 

 

 

 

 

 

 

 

 

 

 

d) (5) r > R3

 

 

 

 

Problem 3: A beam of electrons flies from the left into the magnetic field, perpendicularly to its field lines, which emerge perpendicularly from the plane of the figure and have a magnitude of B = 4.55 10-4 T. The radius of the orbit is r = 3.52 cm.

 

a) (4) Make a drawing of the orbit and mark clearly how exactly the electrons move, including all the directions and orientations.

 

 

 

 

 

 

 

 

 

b) (6) What is the speed v of the circulating electrons? Are relativistic effects significant at this speed?

 

 

 

 

 

 

 

 

 

c) (5) What is the period T of revolution of the circulating electrons?

 

 

 

 

 

 

 

 

 

 

d) (5) What voltage V had to be used to accelerate the electrons from zero to their current speed?

 

 

 

 

 

 

 

Problem 4: An elastic circular conductive loop lies in a plane of drawing, which is perpendicular to uniform magnetic field. The vector of magnetic induction has a direction out of the plane of the drawing and its magnitude B0 = 0.48 T. The area of the loop changes at a constant rate dA/dt = -3.5 10-2 m2/s. At t = 0 the loop has area A = 0.285 m2.

 

a) (4) Make a drawing and mark clearly what will be the direction of the current caused by the EMF induced by the change.

 

 

 

 

 

 

 

 

 

 

b) (6) Determine the induced EMF at time t = 0 s?

 

 

 

 

 

 

 

 

 

 

c) (6) Determine the induced EMF at time t = 2.00 s?

 

 

 

 

 

 

 

 

 

 

d) (4) Let’s cut the loop at one point. What will be the polarity of the EMF on the sides of the cut? Mark it clearly in you drawing or make a new drawing and explain it!

 

 

 

 

Problem 5: Multiple choice. Pick the single best answer to each conceptual question below. Please include a brief explanation. Each answer is worth of 4 credits.

 

1. A current flows in a long straight wire along the x-axis in the positive x-direction. The magnetic field due to this current in a point P on the negative y-axis points to which direction:

a)      –x

b)      +x

c)      –y

d)      +y

e)      –z

f)        +z

 

2. A small planar current loop is placed in a uniform magnetic field. The magnitude of the torque on the loop in a maximum when:

a)      the plane of the loop is parallel to the direction of the field.

b)      the plane of the loop is perpendicular to the direction of the field.

c)      the angle between the plane of the loop and the direction of the magnetic field is somewhere between 0 and 90°.

d)      the torque is independent of the angle between the plane of the loop and the direction of the magnetic field.

 

3. The magnetic energy stored in an inductor is

a)      proportional to the square of the current through the inductor.

b)      proportional to the square of the magnetic field in the inductor.

c)      both of the above.

d)      neither of the above.

 

4. A resistor R and an inductor L are connected in series to a battery, which is switched on at t = 0. The current in the circuit is time-dependent. If we repeat the experiment with a resistor of resistance 5R, the time constant

a)      decreases by the a factor of 5.

b)      increases by the a factor of 5.

c)      does not change.

 

5. A resistor and an initially uncharged capacitor arranged in series are charged by a battery, which is connected at time t = 0. The current in the circuit

a)      is constant because the EMF supplied by the battery is constant.

b)      decreases exponentially in time.

c)      increases exponentially in time.

d)      There is no current because the electrons cannot flow through the gap in the capacitor.