A) Dinesh studying rail guns has been suggested for launching projectiles into space without chemical rockets. A tabletop model rail gun (Figure 1.) consists of two long, parallel, horizontal rails, l= 6.80 cm apart, bridged by a bar of mass m= 8.00 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 = 42.0 A by a power supply that is far to the left of the figure, so it has no magnetic effect on the bar. Figure 1 shows the bar at rest at the midpoint of the rails at the moment the current is established. He wishes to find the speed with which the bar leaves the rails after being released from the midpoint of the rails (Hint: you need to draw the figure). (μ = 47 × 10-T.) V₁=0 m d Figure 1. (i) Find the magnitude of the magnetic field at a distance of 1.85 cm from a single long wire carrying a current of 2.40 A. (ii) 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. (iii) 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 eight times larger than the field at the midpoint. With this assumption, find the magnitude and the direction of the force on the bar.
A) Dinesh studying rail guns has been suggested for launching projectiles into space without chemical rockets. A tabletop model rail gun (Figure 1.) consists of two long, parallel, horizontal rails, l= 6.80 cm apart, bridged by a bar of mass m= 8.00 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 = 42.0 A by a power supply that is far to the left of the figure, so it has no magnetic effect on the bar. Figure 1 shows the bar at rest at the midpoint of the rails at the moment the current is established. He wishes to find the speed with which the bar leaves the rails after being released from the midpoint of the rails (Hint: you need to draw the figure). (μ = 47 × 10-T.) V₁=0 m d Figure 1. (i) Find the magnitude of the magnetic field at a distance of 1.85 cm from a single long wire carrying a current of 2.40 A. (ii) 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. (iii) 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 eight times larger than the field at the midpoint. With this assumption, find the magnitude and the direction of the force on the bar.
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Transcribed Image Text:Question 1:
A) Dinesh studying rail guns has been suggested for launching projectiles into space without
chemical rockets. A tabletop model rail gun (Figure 1.) consists of two long, parallel, horizontal
rails, l= 6.80 cm apart, bridged by a bar of mass m= 8.00 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 = 42.0
A by a power supply that is far to the left of the figure, so it has no magnetic effect on the bar.
Figure 1 shows the bar at rest at the midpoint of the rails at the moment the current is established.
He wishes to find the speed with which the bar leaves the rails after being released from the
midpoint of the rails (Hint: you need to draw the figure). (Mo = 4π × 10-¹T.)
Jg
x
V₁ = = 0
m
d
Figure 1.
(i) Find the magnitude of the magnetic field at a distance of 1.85 cm from a single long wire
carrying a current of 2.40 A.
(ii) 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.
(iii) 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 eight times larger than the field at the midpoint. With this assumption,
find the magnitude and the direction of the force on the bar.
(iv) Explain if the bar is properly modeled as a particle under constant acceleration?
(v) Find the velocity of the bar after it has traveled a distance d= 230 cm to the end of the rails.
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