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Unformatted text preview: HW10
1. (a) Two metal objects are embedded in weakly conducting material of conductivity . Show
that the resistance between them is related to the capacitance of the arrangement by R 0
C (b) Suppose you connected a battery between the two conductors and charge them to a
potential difference V0. If you then disconnect the battery, the charge will gradually leak off.
t / Show that V (t ) V0 e , and find the time constant, , in terms of and .
0 2. A metal bar of mass m slides frictionlessly on two parallel conducting rails a distance l apart.
A resistor R is connected across the rails and a uniform magnetic field B, pointing into the
page, fills the entire region. (a) If the bar moves to the right at speed v, what is the current in the resistor? In what
direction does it flow?
(b) What is the magnetic force on the bar? In what direction?
(c) If the bar starts out with speed v0 at time t=0, and is left to slide, what is its speed at a
later time t? 1 2
(d) The initial kinitic energy of the bar was, of course, 2 mv0 . Check that the energy
1 2
delivered to the resistor is exactly 2 mv0 . 3. A long solenoid of radius a, carrying n turns per unit length, is looped by a wire of with
resistance R, (a) If the current in the solenoid is increasing at a constant rate (dI/dt=k), what
current flows in the loop, and in which direction?
(b) If the current I in the soleinoid is constant but the solenoid is pulled out of the
loop, tuned around, and inserted back to the loop, what total charge passes
through the resistor? 4. Suppose the following circuit has been connected for a long time when suddenly, at time t=0,
switch S is thrown, bypassing the battery. (a) What is the current at any subsequent time t?
(b) What is the total energy delivered to the resistor?
(c) Show that this is equal to the energy originally stored in the inductor. ...
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 Fall '09
 Qiu
 Magnetism, Magnetic Field, Resistor, metal bar, weakly conducting material

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