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 `nu` 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 coverered by the conductor. Magnetic flux `Phi_B =Blx`.

Induced emf `=-(d(Phi_E))/(dt)=-d/(dt)(Blx)`
i.e., `e=-Bl(dx)/(dt)`
But, `(-dx)/(dt)=nu`
`therefore e=Blnu" "` ...........(1)
Note : The Lorentz force acts on a change in a conductor and acts along PQ. done in moving a charge .q. from P to Q is
W= (Lorentz force ) (displacement of the charge .q.)
i.e., W =`(Bqnu)l`
by definition electric p.d `=W/q=(Bqnul)/q=Bnul` ...............(2)
Equation (1) and (2) are identical.