A rectangular loop of wire hangs vertically as shown in the figure. A magnetic f
ID: 1905659 • Letter: A
Question
A rectangular loop of wire hangs vertically as shown in the figure. A magnetic field is di- rected horizontally, perpendicular to the wire, and points out of the page at all points as rep- resented by the symbol ?. The magnetic field is very nearly uniform along the horizon- tal portion of the wire ab (length is 0.3 m) which is near the center of a large magnet producing the field. The top portion of the wire loop is free of the field. The loop hangs from a balance which measures a downward force (in addition to the gravitational force) of 3.56Explanation / Answer
So, the magnetic force on a small element of wire is given by IxB where I is the current in the small element of the wire and B is the magnetic field at that point. By symmetry the forces on the vertical wires cancel out and there is no force on the top wire because it is not in the magnetic field. Now, the force on a small element of the bottom wire (as given by the right hand rule) is directed downward and of magnitude .2B where B is the magnetic field. That is the force on a small element. Thus the force on the whole wire is .2B times the length of the wire, which in this case equals .3 m. So, the net force on the loop is .06B, which is equal to .002163 Newtons. Thus, the magnetic field is 1 T.