FIGURE shows two -turn coils tightly wrapped on the same-diameter cylinder with -diameter wire. The current through coil is shown in the graph. Determine the current in coil at (a) and (b) . A positive current is into the page at the top of a loop. Assume that the magnetic field of coil passes entirely through coil .
a.Current coilat timeis.
b.Current coilat timeis.
Magnetic field for coil is,
Whereis the length of coil.
Whereis the diameter of the wire.
The coil's surface area is,
Because the current is continuous, there is no change in current over time.
That the loop's induced current will be zero.
At, the current changes.
So, between the two points, and the slope is
All values should be substituted,
You’ve decided to make the magnetic projectile launcher shown in FIGURE for your science project. An aluminum bar of length slides along metal rails through a magnetic field The switch closes at , while the bar is at rest, and a battery of emf starts a current flowing around the loop. The battery has internal resistance r. The resistances of the rails and the bar are effectively zero.
a. Show that the bar reaches a terminal speed , and find an expression for .
b. Evaluate for and
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