(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 the10ms intervals shown. (b) In which intervals is the emf not constant? Neglect the 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`.