(a) The magnetic field in a region varies as shown in figure. Calculate the average induce emf in a conducting loop of area 2.0 × 10–3 m2 placed perpendicular to the field in each of the 10 ms intervals shown.
(b) In which intervals is the emf not constant? Neglect the behavior near the ends of 10 ms intervals.
Given:
Area of loop=
We know that
by faraday’s law of electromagnetic induction
Where
ϵ =emf produced
ϕ =flux of magnetic field
so, the average induced emf in the conducting loop between time intervals t1 and t2 is given by
…(ii)
Also
Magnetic flux through the circular ring of area A is given by
Since loop is placed perpendicular to the field,
(i) 
Using eqn.(ii)
. (iii)
Putting the values of 
we get
(ii) 
Using eqn.(ii)
. (iii)
Putting the values of 
we get
(iii) 
Using eqn.(ii)
. (iii)
Putting the values of 
we get
(iv) 
Using eqn.(ii)
. (iii)
Putting the values of 
we get
∴ emf across the intervals
0-10ms =-2mV
10-20ms=-4mV
20-30ms=4mV
30-40ms=2mV
From the graph we can see that flux varies in a nonlinear fashion between time Intervals 10-20 ms and 20-30 ms and hence the derivative of flux wrt time is not constant in the given interval
∴ emf is not constant in time intervals 10-20 ms and 20-30ms