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 This gives
e 
2
1
1 0
2
50
(1 )
=2
×
×
π ×
×
= 157 V
Method II
To calculate the emf, we can imagine a closed loop OPQ in which
point O and P are connected with a resistor R and OQ is the rotating
rod