Determine the direction of the current flow in the loop MPQM while the rod is rotating. Express the emf induced in the loop MPQM as a function of t and the magnitude of the magnetic force acting on the conducting rod OP for 0
Two conducting semicircles, MN and MO, centered at points O and O1 respectively, are
placed on a horizontal plane. The radii of the two semicircles are 4 cm and 2 cm,
respectively. The two semicircles are in electrical contact at point M. A uniform magnetic
field normal to the horizontal plane exists in the region enclosed by the two semicircles
and the line ON, as shown in Figure 2. The magnitude of the magnetic field is
B = 0.015 T. An ultrathin conducting rod has one end electrically connected to the
smaller semicircle MO at point O, and is fixed at point O. The rod has a length equals to
the radius of the larger semicircle, and it rotates clockwise around O at a constant
velocity
good electrical contact with the larger semicircle MN. At t = 0, the end of the rod P is at
point M. For
0
2
t
, as the rod rotates, it is also in good electrical contact with the
smaller semicircle MO at some point Q, as shown in Figure 2. Assume that the
conducting rod has a uniform resistance per unit length, = 5 /m. Neglect the
resistance of the two semicircles.
(i) Determine the direction of the current flow in the loop MPQM while the rod is
rotating.
(ii) Express the emf induced in the loop MPQM as a function of t and the magnitude
of the magnetic force acting on the conducting rod OP for
0
2
t
.
(iii) Find the magnitude of the magnetic force acting on the conducting rod OP for
2
t
.
(iv) Find the work done against the magnetic force from t = 0 to
t
= .
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