Exam 2 practice problems solutions

# You estimate that the probe will take 300 seconds to

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You estimate that the probe will take 300 seconds to descend from orbit (where the magnetic field is zero) to the surface (where the magnetic field has an approximate magnitude of 5 10 T ). Predict the current that will flow in the ring as the probe descends to the surface. Since the probe is descending on the north magnetic pole of the planet the magnetic field lines point directly away from the planet’s surface. I’ll choose the direction of the normal vector of the coil to also point in this direction. I’ll assume the probe is descending with constant velocity and that the magnetic field changes at a constant rate with altitude. , , 2 5 5 cos 0 cos 0 1 1 1 1000 2.00 10 0 4.19 10 10.0 300 0 B f B i f i f i B f i f i f i NB A NB A B B NA I R R t R t t R t t R t t m T I A s      4. A square loop of wire (of negligible resistance) is connected to a light bulb that has a resistance of 10.0 . The magnetic field within the loop is uniform and points perpendicular to the plane of the loop. A graph of the magnetic field is shown (positive values mean the magnetic field points out of the page.) Draw a graph showing the current flowing through the light bulb as a function of time. When there is a current, if ever, predict its value and direction. The magnetic flux through the loop is changing only when the magnetic field is changing, so the only times the bulb will be lit is between 0.3 s and 0.5 s . The only thing I need to calculate then is the current through the bulb between 0.3 s and 0.5 s . 2 2 1 3.0 0.5 0.5 10 0.5 0.3 4.5 B f i f i A B I R R t R t B B s I R t t m T T I s s I A  Since the magnetic field is pointing out of the page and decreasing, the induced magnetic field will also point out of page. This means the induced current will be counterclockwise. I t 4.5 A 0.3 s 0.5 s

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5. You are at a bowling alley picking out the ball you are going to use when you see a highly polished silver colored ball. When you reach down to pick it up you see an image of yourself created by its shiny surface. a. Qualitatively, where is this image located and what are its properties (magnified/demagnified, upright/inverted, etc.)? Include a ray diagram to support your answers. b. If the radius of the ball is 15.0 cm and your face is 35.0 cm from the surface of the ball, numerically determine the location and magnification of the image. The image will form inside the ball. It will be virtual, upright, and demagnified. Mathematically, 1 1 1 1 1 1 7.5 35.0 6.18 6.18 0.177 35.0 i o i i i o d f d d cm cm d cm d cm m d cm       6. You are a safety inspector hired by the Princeton Plasma Physics Laboratory to determine if their new experimental nuclear fusion reactor is generating too strong a magnetic field in nearby offices.
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