Figure shows a circular wheel of radius 10.0 cm whose upper half, shown dark in the figure, is made of iron and the lower half of wood. The two junctions are joined by an iron rod. A uniform magnetic field B of magnitude 2.00 × 10–4 T exists in the space above the central line as suggested by the figure. The wheel is set into pure rolling on the horizontal surface. If it takes 2.00 seconds for the iron part to come down and the wooden part to go up, find the average emf induced during this period.



Given:


Radius of circular wheel r =10cm=0.1m


Magnetic field intensity


Area of semicircular part


Initially



Magnetic flux through the wheel ϕ can be given by formula



Since area vector and magnetic field is parallel we get flux



After time interval Δt=2s



Flux through the wheel



Average induced emf in time interval Δt is given by


…(i)


Where


are flux across the cross section at time intervals respectively.


Therefore, average induced emf ϵ is



Therefore average induced emf in the wheel is


1