Question

A long, rectangular loop of width w, mass m, and resistance R is at rest, with the plane of the loop parallel to the ground. Immediately to the left of the loop is a region of uniform magnetic field B that points into the screen. At time t = 0, a constant force F pushes the loop to the left, into the magnetic field region, as shown in the figure. Derive an expression for the speed v of the loop immediately after it enters the magnetic field region in terms of the given variables and the time t. v = fr / (b^2w^2) 

          A long, rectangular loop of width w, mass m, and resistance R is at rest, with the plane of the loop parallel to the ground. Immediately to the left of the loop is a region of uniform magnetic field B that points into the screen. At time t = 0, a constant force F pushes the loop to the left, into the magnetic field region, as shown in the figure.

Derive an expression for the speed v of the loop immediately after it enters the magnetic field region in terms of the given variables and the time t.

v = fr / (b^2w^2)
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A long, rectangular loop of width w, mass m, and resistance R is at rest, with the plane of the loop parallel to the ground. Immediately to the left of the loop is a region of uniform magnetic field B that points into the screen. At time t = 0, a constant force F pushes the loop to the left, into the magnetic field region, as shown in the figure. Derive an expression for the speed v of the loop immediately after it enters the magnetic field region in terms of the given variables and the time t. v = fr / (b^2w^2)

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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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A long, rectangular loop of width w, mass m, and resistance R is at rest, with the plane of the loop parallel to the ground. Immediately to the left of the loop is a region of uniform magnetic field B that points into the screen. At time t = 0, a constant force F pushes the loop to the left, into the magnetic field region, as shown in the figure. Derive an expression for the speed v of the loop immediately after it enters the magnetic field region in terms of the given variables and the time t.
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Transcript

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00:01 All right, so suppose we have a magnetic field pointing into the page like this, and we have a rectangular loop of wire that is being forced in via the application of a constant force like this, and we're told that the width of the wire is w.
00:19 So we want to find an expression for the speed of the loop after it enters the magnetic field in terms of the time.
00:25 So what we'll have if the loop has a mass m and a resistance r, then the mass times the change in velocity according to newton's law is going to just be the force applied minus the...
00:42 All right, so force on the rectangular section of wire, which is going to be the current times the width times the magnetic field strength, and we can write this furthermore as f minus the current is going to be the emf, which is bwv over r.
00:58 So it's actually going to be...
01:00 Write it as b squared w squared v over r, and so if we solve for the velocity as a function of time by writing this as a differential equation, we'll have that dv over...
01:14 And we'll write it as 1 minus b squared w squared v over f r is going to equal basically m dt over f, i believe.
01:30 All right, so...
01:31 Sorry, this should be f f over m times dt...
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