A rectangular coil ABCD which is rotated at a constant angular veolcity about an horizontal as shown in the figure. The axis of rotation of the coil as well as the magnetic field B are horizontal. Maximum current will flow in the circuit when the plane of the coil is

Options

A. inclined at `30^(@)` to the magnetic field
B. perpendicular to the magnetic field
C. inclined at `45^(@)` to the magnetic field
D. parallel to the magnetic field

Answer

B

Explanation

As the coil is rotated, angle `theta` (angle which is normal to the coil makes with B at any instant t) changes, therefore magnetic flux `phi` linked with the coil changes and hence an emf is induced in the coil. At this instant t, if e is the emf induced in the coil, then
`e=-(dphi)/(dt)=-(d)/(dt)(NBS cos omegat)`
where, N in number of turns in the coil.
or `e=-NSB(d)/(dt)(cosomegat)=-NSB(-sinomegat)omega`
or `e=NBSomega sinomegat` ....(i)
The induced emf will be maximum
when, sin `omega`t i.e., maximum
`therefore" "e_("max")=e_(0)=NSBomegaxx1or e=e_(0)sin omegat`
Therefore, e would be maximum, hence current is maximum (as `i_(0)=e_(0)//R`), when `theta=90^(@)` i.e., normal to plane of coil is perpendicular to the field or plane of coil is parallel to magnetic field.