A square loop `ACDE` of area `20 cm^2 ` resistance `5Omega` is rotate in as magnetic field `B=2T` through `180^@` (a) in `0.01S` and (b) in `0.02 s`
Find the magnitudes of averasge values of e i and `/_\q` in both the cases.

Explanation

Let the take the area vator `S` perpendicular to plane of loop inwards. So initially `dS` parallel to `B` and when it rorated by `180^(@)`, `S` is anti parallel to `B`. Hence, initial flux passing through the loop,
`phi_(i) = BS cos 0^(@) = (2)(20 xx 10^(-4))(1)`
`= 4 xx 10^(-3) Wb`
Flux passing througn the loop when it rotated by
`180^(@), phi_(f) = BS cos 180^(@)`
`= (2) (20 xx 10^(-4))(-1) = -4.0 xx 10^(-3) Wb`
Therefore, change in flux,
`Delta phi_(B) = phi_(f)-phi_(i)`, `= -8 xx 10^(-3) Wb`
(a) Given `Delta t = 0.01 s, R = 5 Omega` , `:. |e| = |(Delta phi_(B))/(Delta t)|`
`= (8 xx 10^(-3))/(0.01) = 0.8V` , or `i = (|e|)/(R ) = (0.8)/(5) = 0.16 A`
and `Delta q = i Delta t = 0.16 xx 0.01`, `= 1.6 xx 10^(-3) C`
(b) `Delta t = 0.02 s`, `:. |e| = |-(Delta phi_(B))/(Delta t)|`
`= (8 xx 10^(-3))/(0.02)`, `= 0.4V`, `i = = (|e|)/(R ) = (0.4)/(5) = 0.08A`
and `Delta q = i Delta t = (0.08)(0.02)`, `= 16 xx 10^(-3)C`