6. Rail guns have been suggested for launching projectiles into space without chemical rockets. A tabletop model rail gun (Figure A2.4) consists of two long, parallel, horizontal rails, l = 3.50 cm apart, bridged by a bar of mass m= 3.00 g that is free to slide without friction. The rails and bar have low electric resistance, and the current is limited to a constant I = 24.0 A by a power supply that is far to the left of the figure, so it has no magnetic effect on the bar. Figure A2.4 shows the bar at rest at the midpoint of the rails at the moment the current is established. We wish to find the speed with which the bar leaves the rails after being released from the midpoint of the rails. (a) Find the magnitude of the magnetic field at a distance of 1.75 cm from a single long wire carrying a current of 2.40 A. (b) For purposes of evaluating the magnetic field, model the rails as infinitely long. Using the result of part (a), find the magnitude and direction of the magnetic field at the midpoint of the bar. (c) Argue that this value of the field will be the same at all positions of the bar to the right of the midpoint of the rails. At other points along the bar, the field is in the same direction as at the midpoint, but is larger in magnitude. Assume the average effective magnetic field along the bar is five times larger than the field at the midpoint. With this assumption, find (d) the magnitude and (e) the direction of the force on the bar. (f) Is the bar properly modelled as a particle under constant acceleration?
6. Rail guns have been suggested for launching projectiles into space without chemical rockets. A tabletop model rail gun (Figure A2.4) consists of two long, parallel, horizontal rails, l = 3.50 cm apart, bridged by a bar of mass m= 3.00 g that is free to slide without friction. The rails and bar have low electric resistance, and the current is limited to a constant I = 24.0 A by a power supply that is far to the left of the figure, so it has no magnetic effect on the bar. Figure A2.4 shows the bar at rest at the midpoint of the rails at the moment the current is established. We wish to find the speed with which the bar leaves the rails after being released from the midpoint of the rails. (a) Find the magnitude of the magnetic field at a distance of 1.75 cm from a single long wire carrying a current of 2.40 A. (b) For purposes of evaluating the magnetic field, model the rails as infinitely long. Using the result of part (a), find the magnitude and direction of the magnetic field at the midpoint of the bar. (c) Argue that this value of the field will be the same at all positions of the bar to the right of the midpoint of the rails. At other points along the bar, the field is in the same direction as at the midpoint, but is larger in magnitude. Assume the average effective magnetic field along the bar is five times larger than the field at the midpoint. With this assumption, find (d) the magnitude and (e) the direction of the force on the bar. (f) Is the bar properly modelled as a particle under constant acceleration?
College Physics
1st Edition
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:Paul Peter Urone, Roger Hinrichs
Chapter20: Electric Current, Resistance, And Ohm's Law
Section: Chapter Questions
Problem 60PE: Integrated Concepts (a) What energy is dissipated by a lightning bolt having a 20,000-A current, a...
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Transcribed Image Text:(g) Find the velocity of the bar after it has travelled a distance d= 130 cm to the end of the rails.
27
·x
V₁=0
m
Figure A2.4
Transcribed Image Text:6. Rail guns have been suggested for launching projectiles into space without chemical rockets. A
tabletop model rail gun (Figure A2.4) consists of two long, parallel, horizontal rails, l= 3.50 cm apart,
bridged by a bar of mass m= 3.00 g that is free to slide without friction. The rails and bar have low
electric resistance, and the current is limited to a constant I = 24.0 A by a power supply that is far
to the left of the figure, so it has no magnetic effect on the bar. Figure A2.4 shows the bar at rest
at the midpoint of the rails at the moment the current is established. We wish to find the speed
with which the bar leaves the rails after being released from the midpoint of the rails.
(a) Find the magnitude of the magnetic field at a distance of 1.75 cm from a single long wire carrying
a current of 2.40 A.
(b) For purposes of evaluating the magnetic field, model the rails as infinitely long. Using the result
of part (a), find the magnitude and direction of the magnetic field at the midpoint of the bar.
(c) Argue that this value of the field will be the same at all positions of the bar to the right of the
midpoint of the rails. At other points along the bar, the field is in the same direction as at the
midpoint, but is larger in magnitude. Assume the average effective magnetic field along the bar is
five times larger than the field at the midpoint. With this assumption, find
(d) the magnitude and
(e) the direction of the force on the bar.
(f) Is the bar properly modelled as a particle under constant acceleration?
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