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 The potential difference across the resistor is then equal to the
induced emf and equals B × (rate of change of area of loop) If q is the
angle between the rod and the radius of the circle at P at time t, the
area of the sector OPQ is given by
2
2
1
2
2
R
R
θ
θ
π
×
=
π
where R is the radius of the circle