A conducting loop of resistance `R` and radius `r` has its center at the origin of the co-ordinate system in a magnetic field of induction `B`. When it is rotated about `Y`-axis through `90^(@)`, net charge flown in the coil is directly proportional to

Options

A. B
B. R
C. `r^(2)`
D. r

Answer

A, C

Explanation

emf is induced when the flux `phi` varies, the variation flux d`phi` during time dt is given as
E = `(d phi)/(dt)`
`rArr int_(phi_(1))^(phi_(2)) d phi = Delta phi = int` Edt `" "` … (1)
`rArr` The total charge flown in the loop = q = `int` i dt
q = `int (E )/(R)` dt `" " ` ... (2)
using (1) and (2)
q = `(Delta phi)/(R)`
Where `Delta phi` = change in flux given as `Delta phi = phi_(2) - phi_(1) = " B. " (pi r^(2))` because intially to flux is linked with the coil and it has maximum flux linkage `phi_(2)` = B `pi r^(2)`when turned through `90^(@)` , the flux is reduced to zero .
`rArr q = (pi B r^(2))/(R)`
`rArr` i.e. q `prop` B
q `prop r^(2)`
q `prop` (1/ R)
Hence (A) & (c ) are correct .