A conducting rod of length 1m is moved in a magnetic field of magnitude B with velocity v such that the arrangement is mutually perpendicular. Prove that the emf induced in the rod is | E | = Blv.

Let us assume a rectangular loop LMNO is placed in a uniform magnetic field B.
Suppose at any instant, length ON = x
Flux through the loop,

straight ϕ equals space Blx

[

because

max, flux,

straight ϕ space equals BA

]
Induced emf,

straight E space equals space minus dϕ over dt space equals space minus straight d over dt Blx

or,

straight E space equals space minus Bl dx over dt space equals negative Blv

Let us assume a rectangular loop LMNO is placed in a uniform magnetic

where

dx over dt space equals space minus straight v comma

is the velocity of conductor MN.

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