In the figure shown there exists a uniform time varying magnetic field `B = [(4 T//s) t + 0.3 T]` in a cylinderical region of radius `4m`. An equilateral traingualr conducting loop is placed in the magnetic field with its centroide on the axis of the field and its plane perpendicular to the field.

Options

A. `e.m.f.` induced in any one rod is `16 V`
B. `e.m.f.` incduced in the complete `Delta ABC` is `48 sqrt(3) V`
C. `e.m.f.` induced in the complete `Delta ABC` is `48V`
D. `e.m.f.` induced in any one rod is `16 sqrt(3) V`

Answer

B, D

Explanation

`e_(AB) = ((dB)/(dt))` area of `Delta AOB`, USING (E.M.I)
`= (4)(1)/(2) xx (4 xx (sqrt(3))/(2) xx 2) xx 2`
total emf of loop `= 3 xx (4 xx (1)/(2) xx 4 xx (sqrt(3))/(2) xx 2) xx 2`
`= 2xx24sqrt(3) = 48sqrt(3) "Volt"`