Fall 2011

Professor: Julie Rathbun

Office: AHON 129

ext. 8661

E-mail: Julie_Rathbun@redlands.edu

Office Hours: MW 11:00 am - noon, F 1:30-2:30 pm, see my schedule for times that I am availible.

Homework will be graded beginning on Wednesdays at 10:30 am. Make sure the "real" homework is turned in by that time, including all problems assigned for the previous week.

**Friday 12/9/11** - Give out take-home final. Due next friday.

**Wednesday 12/7/11** - Go over returned hw.

**Monday 12/5/11** - Final HW due this morning. Conceptual Exam in class.

**Friday 12/2/11** - More problems

1. In Example problem 5.6, we found the magnetic field due to a ring of current. Use that solution to find the magnetic field on the axis of a finite solenoid, inside the solenoid. The solenoid has a radius a and length L and carry surface current density K.

2. A metal rod of length 12 cm and mass 70 grams has metal loops at both ends, which go around two metal poles. The rod is in good electrical contact with the poles but can slide freely up and down. The metal poles are connected by wires to a battery, and a 5 A current flows through the rod. A magnet supplies a large uniform magnetic field B in the region of the rod, large enough that you can neglect the magnetic fields due to the 5 A current. The rod sits at rest 4 cm above the table. What are the magnitude and direction of the magnetic field in the region of the rod?

3. A parallel plate capacitor with circular plates of radius R=30 mm and plate separation of 5.0 mm is connected to a power supply set to deliver a sinusoidal wave with an angular frequency of 60 Hz and maximum voltage of 150 V. For all parts, explicitly check the units.

(a) What is the electric field inside the capacitor as a function of time? What is it's maximum value?

(b) What is the magnetic field inside the capacitor? What is its maximum value?

(c) Plot the magnetic field as a function of distace from the center of the capacitor, out to a distance of 5 cm.

(d) What is the poynting vector inside of the capacitor? What is its maximum value?

**Wednesday 11/30/11** - Review & do problems:

1. (a) Find the electric potential at the center of a circular arc of arbitrary angular size. Why can't this be used to find the electric field at that location?

(b) Find the electric field of a circular ring along the axis of the ring.

(c) Using the answer to (b), find the electric field of a circulr plate along its axis. What's a good test for this? Do it.

2. A sphere of radius R has charge density rho=rho_0 cos(theta) in a spherical coordinate system.

(a) Is this the same charge density as rho=rho 0 cos(phi)? A picture may help.

(b) Find the electric field at a point on the z axis far from the sphere (but not too far).

(c) What calculation would you have to perform to calculate the field at an arbitrary distance?

3. A plate of thickness a that in infinite in the other 2 directions is made from a linear dielectric material with dielectric constant epsilon_r. It has embedded in it a unifrom free charge density rho.

(a) Find the electric displacement everywhere.

(b) Find the electric field.

(c) Find the polarization.

(d) Find the potential difference between the edges of the slab.

(e) Find the location and amount of all bound charge.

(f) Now that you know all the charge, recalculate the electric field.

**Monday 11/28/11** - Go over Exam #2

**Monday 11/21/11** - Update study guide through chapter 8

**Friday 11/18/11** - Read remainder of chapter 8 - do problem 8.5 (parts a and b) and redo example problem 8.4, filling in ALL the missing steps and explain so it all makes sense, in particular:

a. Solve for E using Gauss' law.

b. On page 360 just before eq. 8.35, what volume should you use? Why?

c. If the angular momentum density is not constant, how do you find L?

d. What is the initial angular momentm of the system and where is it located? Final?

e. Why is there a negative sign in the first torque equation?

f. How are torque and angular momentum related?

g. Where's the minus sign come from in La?

**Wednesday 11/16/11** - Read sections 8.1 - 8.2.2 - do problem 8.4 (Hint: use cylindrical coordinates with a in the z-direction) and

1. Find S for a half-watt resistor that is 1 cm long and 2 mm in radius.

2. Consider problem #1 from 11/9/11. For a & b, show explicitly that the units work.

a. What is the energy density inside the capacitor?

b. Calclate the poynting vector inside the capacitor.

3. Redo Example problem 8.2, filling in ALL the missing steps especially on page 354) and explain so it all makes sense, in particular:

a. Show trig for getting last formula on top line of page 354.

b. Explain why equation 8.25 id true.

c. What are the integration limits on this area?

d. Where did they get E (right after eq. 8.25)?

e. Why is only the zz term of the stress tensor needed?

**Monday 11/14/11 - Exam 2 (in class)**

**Friday 11/11/11** - HW due 9:30 am, class time for review

**Wednesday 11/9/11** - Read remainder of section 7.3 - do problem 7.37 and

1.(a) write the magnetic field a distance s from a long, straight wire.

(b) Now consider that wire to be part of the circuit in problem 7.25. What is the magnetic field near that wire, how does it change with time?

(c) Now consider the capacitor in this circuit. Calculate the electric field between the capacitor plates (assume the plates are circular with radius R).

(d) Calculate the magnetic filed between the plates as a function of s and t. Plot this magnetic field as a function of s.

(e) Compare your answers to (b) and (d). How do they relate to Maxwell's correction to Ampere's law?

(f) What is the displacement current between the plates of the capacitor?

2. Derive conservation of charge from Maxwell's equations. Explain how this equation represents conservation of charge.

**Monday 11/7/11** - Read sections 7.2.3-7.2.4 - do problems 7.25 (also, calculate the energy stored in both the inductor and capacitor as a function of time, does it behave as you expect?, how would that change if a resistor is included in the circuit),7.26a-c, and

1. Find the inductance per unit length of a pair of concentric cylindrical conductors (coaxial cable) of radii a and b (a < b). Neglect the field inside the metal.

2. A long straight ware lies on the axis of a toroid of N turns and of major and minor radii a and b, respectively. Find the mutual inductance assuming constant B inside the toroid.

3. A square loop of side s lies in the plane of a long wire, at distance a from it. Find the mutual inductance. Evaluate for a = 1 cm and s = 3 cm.

**Friday 11/4/11** - Read sections 7.2.1-7.2.2 - do problems 7.13 (except in the 2nd quadrant: +x, -y; AND give the direction of the induced current), 7.17, and

1. An infinite solenoid with 1700 turns per meter and a radius of 2 cm carries a current that increases linearly from 0 to 1.2 A in 0.4 s. Find the emf in a single loop of wire with a radius of 3 cm that is around the solenoid.

2. A rectangular loop of wire (20 mm x 10 mm) with resistance of 20m Ohms is rotating at a rate of 2 rad/s around one of the long arms of the loop. This rotating loop sits in a constant magnetic field that points in a direction perpendicular to the rotation axis. What is the maximum current induced in the loop? How does it change with time?

3. The electric field in some region is constant and in the phi direction in a cylindrical coordinate system. Sketch this electric field. What magnetic field must be in the same region? Sketch the magnetic field in a different color.

**Wednesday 11/2/11** - Read remainder of section 7.1 - do problem 7.9, and:

1. Imagine that you have two metal rails 20 am apart connected by a light bulb. The rails are places in a 1.0 T magnetic field oriented downward (perpendicular to the rails and the lightbulb). A metal bar slides on the rails toward the light bulb, which has a resistance R=10 ohms.

(a) How fast must the bar move to put a potential difference of 3.0 V acoss the bulb?

(b)In what direction dows the current flow?

(c)What is the magnetic force on the bar (including direction)? What happens to the bar?

(d)What is the bar's speed at a function of time (you must solve a differential equation)?

(e)If the bar has a mass of 100 g, what is it's speed after 30 seconds? Show explicitly that the units work.

(f) The initial energy of the bar is .5mv_i^2, show that the energy delivered to the resistor is the same.

2. A rectangular loop of wire is sitting 4 cm from a very long wire carrying a current of 3A. The loop is 5 cm long parallel to the long wire and 4 cm in the other direction.

(a)It is moving at 20 cm/s toward the long wire. Find the emf (incluting direction) in the loop.

(b)If the loop isn't moving, find the rate at which the current in the long wire must change in order to give the same emf as in part a.

3. The magnetic drag force due to eddy currents on a conducting plate moving through a magnetic field means that a plate dropped vertically between the poles of a magnet will reach a terminal speed, just like an object falling in air. Auppose we drop a long strip of aluminum half a centimeter thick whose mass is 0.60 kg so that it falls vertically between the poles of a horseshoe magnet. If the poles are round and have a diameter of 5 cm with a field strength of 0.5 T, what is the plate's terminal speed?

**Monday 10/31/11** - Read section 7.1.1 - do problems 7.1ab, 7.2, redo example 7.1 (show that resistance is 2k/3*sqrt(A^3/pi)) with a conductivity which is non-constant, it =ks (where k is a constant), and:

Assume that the top globe of a Van deGraaff generator (Which we can model as a spere 30 cm in daimeter) is charged to the maximum potential it can have relative to infinity without causing the air surrounding it to break down (1 MegaVolt per meter). A person (with a resistance of 10,000 ohms) touches the globe while it tis charged. Draw a circuit diagram of this situation. What is the maximum current that flows thru the person? For how long? Given that a 50mA current maintained for more than a few seconds can kill a person, is the person risking death?

**Friday 10/28/11** - Pretty Equation sheet due that compares Electricity to Magnetism and summarizes what we've learned so far.

**Wednesday 10/26/11** - Go thru EVERY homework. For each problem, write a one-sentence description of what the main point of the problem is AND write the major equations used.

**Monday 10/24/11** - Read section 6.3-6.4 (skip 6.3.3) - do problems 6.12 (use technique from example problem 5.9), 6.16, 6.17, 6.20, 6.25 (set a=x/y and derive a trancendental equation for a, use wolfram to get a)

**Friday 10/21/11** - Read sections 6.1-6.2 - do problems 6.1, 6.7, 6.8, 6.9

**Wednesday 10/19/11** - Read section 5.4 - do problems 5.23, 5.34, 5.35, 5.36

**Monday 10/17/11** - Read section 5.3 - do problems 5.14, 5.15, 5.16, 5.19

**Friday 10/14/11** - Read section 5.2 - do problems 5.9, 5.11, 5.12

**Wednesday 10/12/11** - Read section 5.1 - do problems 5.1, 5.3, 5.4, 5.5, 5.6

**Monday 10/3/11 - Exam 1**

**Friday 9/30/11** - Read section 4.4 (skip 4.4.2) - do problems 4.18, 4.20 (free charge only out to R) 4.26

**Wednesday 9/28/11** - Read sections 4.2-4.3 - do problems 4.10, 4.11, 4.14, 4.15

**Monday 9/26/11** Read section 4.1 - do problems 4.1, 4.4, 4.5

**Friday 9/23/11** - Read section 3.4 - do problems 3.26, 3.30, 3.31

**Wednesday 9/21/11** - Read section 2.5 - do problems 2.35, 2.36, 2.39, 2.43

**Monday 9/19/11** continue with 2.4

**Friday 9/16/11** - Read section 2.4 - do problems 2.31 and 2.32

**Wednesday 9/14/11** - Read section 2.3 - do problems 2.21 (be careful, the formula for the electric field changes along the integration path), 2.22 (why can't you use s=inf as your reference point?), 2.25 a (should be two positive charges, like 2.2) and b, 2.28 (take a careful look at example problem 2.7)

**Monday 9/12/11** - Read sections 2.1-2.2 - do problems 1.7, 2.2, 2.3, 2.14, 2.16

**Friday 9/9/11** - Read chapter 1 - do problems 1.27 and 1.39

Some of the material on this page is in PDF format. If your computer does
not already have it, you will need to download Adobe Acrobat Reader
(free software) to view that content.

Updated 9/8/03