A long, narrow rectangular loop of wire is moving toward the bottom of the page

Question

A long, narrow rectangular loop of wire is moving toward the bottom of the page with a speed of 0.021 m/s (see the drawing). The loop is leaving a region in which a 2.1 T magnetic field exists; the magnetic field outside this region is zero. During a time of 3.0 s, what is the magnitude of the change in the magnetic flux?

A long, narrow rectangular loop of wire is moving toward the bottom of the page with a speed of 0.021 m/s (see the drawing). The loop is leaving a region in which a 2.1 T magnetic field exists; the magnetic field outside this region is zero. During a time of 3.0 s, what is the magnitude of the change in the magnetic flux?

Explanation / Answer

The change in flux linking the loop is:

?? = B*?A

where ? is the flux, B is the flux density, and ?A is the area change.

?A = x*?y = x*(?y/?t)*?t

Note that ?y/?t is the stated velocity, "v":

?A = x*v*?t

?? = B*x*v*?t = 2*x*.023*2 = .092*x webers

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