# The magnetic field between the metal rails as shown below is uniform

Physics 2202-101

1) The magnetic field between the metal rails as shown below is uniform and directed

into the page. It has magnitude 0.3 T. The metal bar can slide with minimal friction while

still maintaining electrical contact at both ends with the rails. Someone pushing (or

pulling ) the bar can induce current in the external resistor attached as shown. The bar

and rails have negligible resistance.

a) How much current flows in the resistor if the rate of thermal energy produced in the

resistor is 5 Watts?  Determine the induced  EMF and the speed (assumed constant) at

which the bar is sliding.

b) What effect does the direction of motion have on the behavior of the circuit? Discuss

and be specific.

c) How much force has to be applied to generate 5 Watts of thermal power as described?

Describe the motion of the bar if the person stopped pushing while the bar was in motion.

Are any forces still acting on the bar once the person stops pushing? Discuss.

2)  A 0.3 kg bar slides vertically down a set of rails at a terminal speed v while a 1.24 m

section of the bar is immersed in a uniform magnetic field of magnitude 0.4 T directed

horizontally ( out of the page).  The resistance of the bar is 0.2 O . The rails have

resistance 0.4 O.

a) Determine v.

b) In which direction does the induced current flow? Be specific and explain how you

know.

c) Compare, through calculation, the amount of work done on the bar by gravity to the

thermal (internal) energy generated in the bar and the rails as the bar falls 0.5 m.

3) Imagine a bar magnet that is dropped and falls through a very compact, tightly wound

coil.Even though the magnetic field of the magnet is constant in time to an observer at

rest with the magnet, an observer at rest with the coil  will observe a magnetic field

across the cross-section of the coil that varies with time. As a result, this second observer

would record a time varying flux through the coil cross-section. The graph below

represents an idealized representation of how the flux would vary with time as the magnet

falls through the coil. Positive flux here is associated with field lines that point in the

positive z direction, so imagine an observer looking into the coil from below.

a) Consider each section of graph where the flux is constant.  Where must the magnet be

relative to the coil during each of these segments? Make sketches so I know exactly what

you mean and explain your reasoning.

b) Sketch a graph of the induced EMF in the coil versus time. It should clear how your

graph correlates with the graph of f versus time. A positive EMF corresponds to

counterclockwise current circulation as seen by an observer looking up into the coil.

4) The larger circle in the diagram below represents a coil that is part of a circuit

containing a DC voltage source. The smaller circle represents a second coil that is placed

inside the larger coil. It is also part of a circuit, but this circuit does not include a voltage

source. The second coil has 400 turns of wire and a diameter of 15 cm. Initially the larger

coil is disconnected from the voltage source but as soon as a connecting switch is closed

the current in the coil begins to rise according to:

time and a=0.34 s

-1

I(t) = 0.6amps(1- e

-at

. The resulting magnetic field (directed out of the page) depends on I according to:

B(I) = (0.47

Tesla amp) where t is the )I and is uniform over the cross section of the larger coil.

a) Derive a formula for the induced EMF in the smaller coil as a function of time.

b) In which direction will current flow in the smaller coil? Explain how you know.

c) Will this induced current increase, decrease or stay the same over time? Explain your

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