(a) the magnetic field in a region varies as shown in . Calculate the average induced emf in a conducting loop of area `2.0X10^(-3) m^2` placed perpendicular to the field in each of the`10ms` intervals shown. (b) In which intervals is the emf not constant? Neglect behaviour near the ends of 10 ms intervals.

Explanation

(a)` phi_2=B.A=00.01xx2xx10^(-3)`
`=2xx10^(-5) [since phi_1=0]`
`d phi=2xx10^(-5)`
`e=(-d phi)/(dt)=(-2xx10^(-5))/(10xx10^(-3))`
`=2xx10^(-3)=-2 mV`
`phi_3=B.A= 0.04xx2xx10^(-3)`
`=6xx10^(-5)`
`d phi = 4xx10^(-5)`
`e=(-d phi)/(dt)=-4mV`
`phi_4=B.A=0.01xx2xx10^(-3)`
`=2xx10^(-5)`
`d phi=-4xx10^(-5)`
`e=-(d phi)/(dt)=4mV`
`phi_5=B.A=0`
`d phi =-2xx10^(-5)`
`e=(-d phi)/(dt)=-((-2)xx10^(-5))/10xx10^(-3)=2mV.`
`(b) Emf is not constant is case of rarr 10-20ms and 20 ms - 30 ms as -4 mV and 4 m`.