Motional Emf

Question based on Motional Electro motive force (emf)

A metal rod is falling toward the surface of the Earth near the equator. As it falls, one end of the rod become positively charged due to the motional emf of the rod through the Earth's magnetic field. The rod is oriented so that

With the help of a neatly drawn labelled diagram, prove that the magnitude of motional emf .e. is given by e=Blv, where .I. is the length of a metallic rod and v is the velocity with which it is pulled in a transverse magnetic field .B..

A wire forming one cycle of sine curve is moved in x-y plane with velocity vec(V)=V_(x)hat(i)+V_(y)hat(j) . There exist a magnetic field vec(B)=-B_(0)hat(k) . Find the motional emf decelop across the ends PQ of wire.

What is motional e.m.f ? State any two factors on which it depends

Assertion : Motional induced emf e = Bvl can be derived from the relation e = -(dtheta)/(dt) Reason : Lenz's law is a consequence of law of conservation of energy.

Assertion : Motional induced emf e = Bvl can be derived from the relation e = -(d\phi)/(dt) Reason : Lenz's law is a consequence of law of conservation of energy.

Give the explanation of reason behind the origin of motional induced emf.