Derive the expression for emf induced in a straight conductor moving perpendicular to a uniform magnetic field.

Explanation

Consider metallic frame MSRN placed in a uniform constant magnetic field. Let the magnetic field B be perpendicualr to the plane of the coil. Let a metal rod PQ of length .l. placed on it be moving towards left with a velocity v as shown in the figure. Let the distance of PQ from SR be x
The magnetic flux linked with the area SPQR is
`phi_(B)=BA cos theta`
`="Bl"x cos0="Bl"x`
As the rod PQ is moving towards left with a velocity v, x is changing and
`vec(v)=(-dx)/(dt)" "_ _ _ _ _(1)`
Hence Induced emf `epsilon=(-d phi_(B))/(dt)=(-d(Blx))/(dt)=-Bl(dx)/(dt)`
`impliesepsilon=Blv" "(because" eqn "(1))`
This emf is induced in the rod because of the motion of the rod in the magnetic field. Therefore this emf is called motional emf.