Electric Charges And Fields

Question

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.

Solution

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,

ϕ = Blx

[

∵

Magnetic flux,

ϕ = BA

]

Therefore,

Induced emf,

E = - \frac{dϕ}{dt} = - \frac{d}{dt} Blx

\Rightarrow

E = - Bl \frac{dx}{dt} = - Blv

where

\frac{dx}{dt} = - v,

is the velocity across the conductor MN.