Question

A conducting rod of length l is moved in a magnetic field of magnitude B with velocity V.

Prove that the emf induced in the rod is |E| = B / V

Answer 1

the force on a charge particle in magnetic field is given as

F = q (v X B)

now, an electrostatic field is generated which exerts a force F = qE on the particle

so,

qE = q (v X B)

or

E = v X B

or in other terms

E = vB

the potential difference is given as V = El

so,

V = vlB

this potential difference is equivalent to the motional emf this,

ε = V

thus, finally we get

ε = B.l.v