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36. The drawing shows that a
uniform magnetic field is directed perpendicularly into the plane of the
paper and fills the entire region to the left of the y axis.
There is no magnetic field to the right of the y axis.
A rigid right triangle ABC
is made of copper wire. The triangle rotates counterclockwise about the
origin at point C. What is the direction (clockwise or counterclockwise) of the
induced current when the triangle is crossing (a) the + y axis, (b) the - x axis, (c) the - y axis, and (d) the + x axis? For
each case, justify your answer. |
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Crossing +y axis: |
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As the triangle crosses the +y
axis, the magnetic field in the triangle is going from nothing to something
and so, the magnetic flux will increase as more of the triangle’s area is
passing into the magnetic field. Lenz’s
law tells us that the induced current in the triangle will seek to oppose the
change in flux and so it will create a field in the opposite direction of the
increasing field. Since the increasing
field is into the paper, the induced field will be out of the paper and by
the right hand rule the current in the triangle will flow Counter-Clockwise! |
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Crossing –x axis: |
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As the triangle crosses the –x axis, the magnetic field passing through the triangle
remains constant so the magnetic flux remains constant. Since there is no change in magnetic flux,
there is no induced current! |
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Crossing –y axis: |
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As the triangle crosses the –y
axis, the magnetic field is now decreasing and therefore the magnetic flux is
decreasing. To oppose the change in
magnetic flux the induced current must create a magnetic field in the same
direction as the original magnetic field, therefore into the paper. To create a field into the paper the
current in the triangle must go Clockwise! |
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Crossing +x axis: |
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As the triangle crosses the +x axis, once again there is no change in magnetic field
strength passing through the triangle as there is no magnetic field in this
region. Therefore
there will be no induced current! |
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