Electricity and Magnetism Resource Packet (comments to: moloney@nextwork.rose-hulman.edu)

Suggestions for 'Active' Classroom Learning

Consider the electric field described by the field lines shown in the figure. The force F on a positive test charge Q placed at position O is shown.

(a) Draw additional force vectors to indicate the magnitude and direction on this test charge when it is placed at points A, B, and C. Scale the length of your force vectors relative to the force F shown. (If the force is zero, state this explicitly.)

(b) A test charge -Q is placed at point D. Indicate the force acting on it.

Given three charges of equal magnitude, two positive and one negative. Can these charges be arranged along a straight line so that there is at least one point of stable equilibrium for a fourth (positive) test charge free to move along the straight line?
Suppose there were a constant electric field given by E=iExo +0j+0k. Find the electric potential difference between the point (0,0,0) and (a,b,c).

[V(abc)-V(000) = - a Exo] .

The picture at the right shows equally-spaced voltage contours from 3 charges.
a) Which charges have the same sign?
What is the evidence for this conclusion?

b) Roughly what are the relative magnitudes of A, B, and C?

c) Where is the electric field largest?

d) Where is the electric field smallest?

[a) A & B b) A, B < C c) Near A, B, and C, and also between C and each of the other 2 charges. d) Between A and B, and above A and B.]

Electric potential (V) is plotted as a function of distance in 1-D. The electric potential is zero outside the region shown.

a) Based on this plot, sketch electric field as a function of distance. What was your reasoning in constructing this graph?

b) Where are the electric charges which create the electric field and electric potential?

c) What are the values of the charges causing the graph shown?

DC Circuits.
The circuits show partial student solutions for currents. The solutions may be correct or in error. If possible, find the current all the branches of the circuit. If no consistent values are possible explain where the self contradiction arise.

(See Fig 4.) The circuits show partial student solutions for potential changes. The solutions may be correct or in error. If possible, find the potential drop across all the circuit elements of the circuit. Also indicate with a + sign the more positive end of each circuit element. If no consistent values are possible explain where the self contradiction arises.

A 12-v battery is connected across points A and B in each of the figures. Each resistor has a value of R ohms. a) Will the current be the same in each case between points A and B? Give your reasoning.
b) Call the current in the righthand picture Io. Find the current in each resistor on the left in terms of Io.

[a) No, more current will flow on the left, where more paths are available. b) The current is Io/3 in all resistors except the one straight down the middle, which still has current Io.]

Two students are arguing about a possible design for a speaker. A thin rectangular slab of moderately resistive material is connected to a power supply at the midpoints of two opposite sides. One student says that the current will distribute itself uniformly and flow from top to bottom in a uniform sheet. The other student argues that all the current will just flow down the center of the rectangle. What do you think? [Neither student is correct. This situation is similar to that of the previous problem.]

Our goal is to prove that the magnetic field produced by a very long straight wire of finite radius is tangent to a circle whose center is the center of the wire. We do this by considering the wire to be a bundle of infinitesimally thin wires. Find the magnetic field due to one of these wires (1) at some point p. Express this field in components, one parallel to a line from the center of the wire to p, the other perpendicular to it. Calculate the field due to another wire, (2) suitably chosen to cancel one component of the first field. Will this proof also work for points inside the wire?

Two infinitely long parallel wires each carry a current I in the same direction.
The centers are a distance d apart.
At what points could the magnetic field from these two wires be zero?
a) along the line joining the wires at a point like p1 between the wires
b) along the line joining the wires at a point like p2 outside the wires
c) at a point like p3 not on the line joining the wires like
d) at no point

The sketch shows a long wire carrying a current which turns on and off due to the transmission of digital data. Three coils are shown near the wire, each intended to 'pick up' information from the wire. Which one will be the most successful and which the least successful? [All three are circular, outside the wire, oriented in different directions.]

Some mad scientist claims that this result leads him to conclude that you can get free electricity by putting such a loop in the vicinity of the power lines going from the generator to the customers. What's wrong with this mad man's suggestion?

[It's not legal to 'tap' the power company's lines, though it is possible to extract energy by this means.
The loop is a little like the 'secondary' of a transformer.]