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 Hence, the induced emf is
e = B
t
R
×


dd
1
2
2θ  = 
2
2
1
d
2
d
2
θ
ω
= B R
BR
t
[Note: 
d
2
dt
θ
ω
ν
=
=
π
]
This expression is identical to the expression obtained by Method I
and we get the same value of e Rationalised 2023-24
Electromagnetic
Induction
165
 EXAMPLE 6 7
Example 6