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**10. Review Conceptual Example 3 and Figure 22.7b. A conducting rod slides down between two frictionless
vertical copper tracks at a constant speed of 4.0 m/s perpendicular to a
0.50-T magnetic field. The resistance of the rod and tracks
is negligible. The rod maintains electrical contact with
the tracks at all times and has a length of 1.3 m. A 0.75-Ω
resistor is attached between the tops of the tracks.
(a)
What is the mass of the rod? (b) Find
the change in the gravitational potential energy that occurs in a time of
0.20 s. (c)
Find the electrical energy dissipated in the resistor in 0.20 s. |
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Since the speed of the mass
falling is constant and we know gravity is acting, the magnetic force must be
acting up to oppose gravity and produce a zero acceleration. Now, the current is induced as shown can
also be determined by using Lenz’s law which says that the induced current
must create a magnetic field which opposes the change in magnetic flux. Since as the rod falls the loop it makes
electrically must be getting larger, the constant magnetic field passing
through an increasing area must make a larger magnetic flux. So the induced current
must create a magnetic field that is opposing the external field in an
attempt to keep the magnetic flux constant.
So the induced current must go the direction
as shown so that its magnetic field is opposite to the external magnetic
field. Again using the right hand
rule! |
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Magnetic force is gotten from |
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Magnitude of this is |
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Angle is 90° as L is in the direction of the
current which is perpendicular to B in the is case. |
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We can get current from Ohm’s
law |
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We get emf
from |
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So current is |
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And magnetic force is |
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Now we can find mass using sum
of forces |
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Solving for mass |
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Change in gravitational
potential in 0.20 s, |
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- sign due to falling a
distance d, which we find from standard kinematics |
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Energy dissipated in 0.20 s,
is due to the consumption of power |
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Same as change in
gravitational potential energy as it should be! |
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