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

Explanation

The rod of length l is moved through a distance x with constant velocity .v. perpendicular to the uniform magnetic field B.
The magnetic flux `phi_B` enclosed by the loop is
`phi_B` = B x area of the loop
`phi_B=Blx`
According to Faraday.s law , induced emf in the coil is `E=(dphi_B)/(dt)`
`E=(d(Blx))/(dt)`
E=Blv [Because `-(dx)/(dt)=v` ]

Let .PQ. represent a conductor moving with a speed .v. at right angles to the magneic flux density .B. pointing perpendicular to the sheet of the paper and pointing towards the paper . Let RQ=x be the distance covered by the conductor . Magnetic flux `phi_B=Blx`.
Induced emf , `e=-(d(phi_E))/(dt)=-d/(dt)(Blx)`
i.e., `e=-Bl (dx)/(dt)`
But, `(-dx)/(dt)=0`
e=Blv