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

Explanation

Let .PQ. represent a conductor moving with a speed .V. at right angles to the magnetic flux density .B. pointing perpendicular to the sheet of paper and pointing towards the paper .Let RQ = x be the distance covered by the conductor .Magnetic flux ` phi _(B ) = B //x .`
Induced emf `=- (d{phi _(E )))/(dt ) =-(d )/(dt ) (b//x )`
` i,e., e=- Bl (dx)/(dt)`

But , ` (-dx )/(dt) = v `
` therefore e= B/v `
Note : The Lorentz force acts on a charge in a conductor and acts along PQ. Work done in moving a charge .q. from P to Q is
W= (Lorentz force )(displacement of the charge .q. ).
i.e., W = (Bqv )l
By definition electric p.d
`=(W)/(q)=(Bqvl)/(q)=Bvl`
Equation (1) and (2) are identical .