In given figure, a wire loop has been bent so that it has three segments ab (a quarter circle), bc (a square corner) & ca (straight line). Here are three choices for a magnetic field through the loop -

(1) `vec_(B_(1))=3hati+7hatj-5thatk`
(2) `vec(B_(2))=5thati-4hatj-15hatk`
(3) `vec(B_(3))=2hati-5thatj-12hatk`
where B is in milli tesla and t is in second. If the induced current in the loop due to `vec(B_(1)),vec(B_(2)),vec(B_(3))` are `i_(1), i_(2), i_(3)` respectively then

Options

A. `i_(1)gti_(2)gti_(3)`
B. `i_(2)gti_(1)gti_(3)`
C. `i_(3)gti_(2)gti_(1)`
D. `i_(1)=i_(2)=i_(3)`

Answer

2

Explanation

`i_(1)=(dphi_(1))/(dt)(1)/(R)=(d[B_(1)xxArea])/(Rdt)`
`=(d)/(dt)[5txx(pia^(2))/(4)]xx(1)/(R)=(5pia^(2))/(4R)`
`i_(2)=(dphi_(2))/(dt)xx(1)/(R)=(d[5a^(2)t])/(dt)xx(1)/(R)=(5a^(2))/(R)`
`i_(3)=(dphi_(3))/(dt)xx(1)/(R)=(d[0.5a^(2)])/(dt)xx(1)/(R)=(a^(2))/(R)`
`thereforei_(2)gti_(1)gti_(3)`