A wire 88cm long bent into a circular loop is placed perpendicular to the magnetic field of density 2.5 Wb `m^(-2)`. Within 0.5 s the loop is changed into square of each side 22 cm and the density is increased to `3Wbm-2`. Calculate the value of e.m.f. induced.

Explanation

Length of wire = 88 cm
It is bent into the form of a circular loop.
Let r=radius of loop
`2 pi r=88`
`rArr r=(88)/(2 pi)`
`rArr r=(88xx7)/(2xx22)=14 cm`
Area of circular coil `=A_(1)= pi r^(2)`
`=(22)/(7) (14)^(2)`
`=616 cm^(2)=616xx10^(-4) m^(2)`
`B_(1)=2 cdot 5" wbm"^(-2)`
`phi_(1) =B_(1)A_(1)=616xx10^(-4)xx2 cdot5`
`=1540 xx10^(-4)`
Then it is bent in the form of a square having each side 22 cm.
So Area of square loop `=A_(2)="(side)"^(2)=(22)^(2)`
`A_(2)=484 cm^(2)=484xx10^(-4) m^(2)`
`B_(2)=3" wbm"^(-2)`
`phi_(2) =B_(2)A_(2)`
`=3xx484 xx10^(-4)`
`=1452 xx10^(-4)` wb
`dt=0 cdot 5` s
`e=-((phi_(2)-phi_(1)))/(dt)`
`=((1452xx10^(-4)-1540 xx10^(-4)))/(0 cdot 5)`
`=-((1452-1540)10^(-4))/(0 cdot 5)`
`=(-(-88)xx10^(-4))/(0 cdot 5) =176xx10^(-4)` volt
`=0 cdot 0176` volt