AP Free Response Question
2008 B3
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A rectangular wire loop is connected across a power supply with an internal resistance of 0.50 ohms and an emf of 16 V. The wire has resistivity 1.7 x 10
^{-8}
ohm-m and cross-sectional area 3.5 x 10
^{-9}
m
^{2}
. When the power supply is turned on, the current in the wire is 4.0 A.
(a) Calculate the length of wire used to make the loop.
The wire loop is then used in an experiment to measure the strength of the magnetic field between the poles of a magnet. The magnet is placed on a digital balance, and the wire loop is held fixed between the poles of the magnet, as shown below. The 0.020 m long horizontal segment of the loop is midway between the poles and perpendicular to the direction of the magnetic field. The power supply in the loop is turned on, so that the 4.0 A current is in the direction shown.
(b) In which direction is the force on the magnet due to the current in the wire segment? ____Upward ____Downward Justify your answer.
(c) The reading on the balance changed by 0.060 N when the power supply was turned on. Calculate the strength of the magnetic field.
Suppose that various rectangular loops with the same total length of wire as found in part (a) were constructed such that the lengths of the horizontal segments of the wire loops varied between 0.02 m and 0.10 m. The horizontal segment of each loop was always centered between the poles, and the current in each loop was always 4.0 A. The following graph represents the theoretical relationship between the magnitude of the force on the magnet and the length of the wire.
(d) On the graph shown above, sketch a possible relationship between the magnitude of the force on the magnet and the length of the wire segment if the wire segments were misaligned and placed at a constant non-perpendicular angle to the magnetic field, as shown below.
Suppose the loops are correctly placed perpendicular to the field and the following data are obtained.
(e) Describe a likely cause of the discrepancy between the data and the theoretical relationship.
Topic Formulas
Description
Published Formula
capacitors in parallel
capacitors in series
electric current
Faraday's Law
friction
gravitational potential energy
Hooke's Law
Joule's Law
magnetic field around a current-carrying wire
magnetic flux
magnetic force on a current-carrying wire
magnetic force on a moving charge
Newton's 2nd Law
Newton's Law of Universal Gravitation
Ohm's Law
resistance in parallel
resistance in series
resistivity
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