A Simple Way to Measure Magnetic Fields A loop of wire is at the edge of a region of space containing a uniform magnetic field B. The plane of the loop is perpendicular to the magnetic field. Now the loop is pulled out of this region in such a way that the area A of the coil inside the magnetic field region is decreasing at the constant rate c. That is, dAdt=−c, with c>0.
A. The induced emf in the loop is measured to be V. What is the magnitude B of the magnetic field that the loop was in?
Express your answer in terms of some or all of the variables A, c, and V.
B. For the case of a square loop of side length L being pulled out of the magnetic field with constant speed v, what is the rate of change of area c=−dAdt?
Express your answer in terms of L and v.
C. Later, you will learn, if you have not already, that the "motional emf" E associated with a rod of length L moving through a uniform magnetic field of magnitude Bwith speed v is given by:
E=vLB,
or, equivalently,
B=EvL.
This is another way of thinking about the result derived above. If you have already studied this, can you see which sides of the square loop contribute to the motional emf and which do not, and why?