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Unreasonable Results
A charged particle having mass $6\text{.}\text{64}\times {\text{10}}^{-\text{27}}\phantom{\rule{0.25em}{0ex}}\text{kg}$ (that of a helium atom) moving at $8\text{.}\text{70}\times {\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ perpendicular to a 1.50-T magnetic field travels in a circular path of radius 16.0 mm. (a) What is the charge of the particle? (b) What is unreasonable about this result? (c) Which assumptions are responsible?
Unreasonable Results
An inventor wants to generate 120-V power by moving a 1.00-m-long wire perpendicular to the Earth’s $5\text{.}\text{00}\times {\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}\mathrm{T}$ field. (a) Find the speed with which the wire must move. (b) What is unreasonable about this result? (c) Which assumption is responsible?
(a) $\text{2.40}\times {\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{m/s}$
(b) The speed is too high to be practical $\le $ 1% speed of light
(c) The assumption that you could reasonably generate such a voltage with a single wire in the Earth’s field is unreasonable
Unreasonable Results
Frustrated by the small Hall voltage obtained in blood flow measurements, a medical physicist decides to increase the applied magnetic field strength to get a 0.500-V output for blood moving at 30.0 cm/s in a 1.50-cm-diameter vessel. (a) What magnetic field strength is needed? (b) What is unreasonable about this result? (c) Which premise is responsible?
Unreasonable Results
A surveyor 100 m from a long straight 200-kV DC power line suspects that its magnetic field may equal that of the Earth and affect compass readings. (a) Calculate the current in the wire needed to create a $5\text{.}\text{00}\times {\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}\mathrm{T}$ field at this distance. (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?
(a) 25.0 kA
(b) This current is unreasonably high. It implies a total power delivery in the line of 50.0x10^9 W, which is much too high for standard transmission lines.
(c)100 metersis along distanceto obtainthe requiredfield strength.Also coaxialcables areused fortransmission linesso thatthere isvirtually nofield forDC powerlines, becauseof cancellationfrom opposingcurrents. Thesurveyor’s concernsare nota problemfor hismagnetic fieldmeasurements.
Construct Your Own Problem
Consider a mass separator that applies a magnetic field perpendicular to the velocity of ions and separates the ions based on the radius of curvature of their paths in the field. Construct a problem in which you calculate the magnetic field strength needed to separate two ions that differ in mass, but not charge, and have the same initial velocity. Among the things to consider are the types of ions, the velocities they can be given before entering the magnetic field, and a reasonable value for the radius of curvature of the paths they follow. In addition, calculate the separation distance between the ions at the point where they are detected.
Construct Your Own Problem
Consider using the torque on a current-carrying coil in a magnetic field to detect relatively small magnetic fields (less than the field of the Earth, for example). Construct a problem in which you calculate the maximum torque on a current-carrying loop in a magnetic field. Among the things to be considered are the size of the coil, the number of loops it has, the current you pass through the coil, and the size of the field you wish to detect. Discuss whether the torque produced is large enough to be effectively measured. Your instructor may also wish for you to consider the effects, if any, of the field produced by the coil on the surroundings that could affect detection of the small field.
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