Using Eq (6 5), the magnitude of the
emf generated across a length dr of the rod as it moves at right angles
to the magnetic field is given by
d
Bvd
r
ε = Hence,
ε
ε
=
= ∫
∫
d
Bvd
r
R
0
 =
=
∫ B
r
r
B
R
R
ω
ω
d
2
0
2
Note that we have used v = w r