Question

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

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

Answer 1

Induced emf loop when the variation of 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.(pir^(2))` because intially to flux is linked with the coil and it has maximum flux linkage `phi_(2)=B pir^(2)` when turned through `90^(@)`, the flux is reduced to zero.
`rArr q=(piBr^(2))/(R )`
i.e. `q prop BrArr q prop r^(2) rArr q prop (1//R)`