A loop made of straight edges has six corners at `A(0,0,0), B(L, O,0), C(L,L,0), D(0,L,0), E(0,L,L)` and `F(0,0,L)`. Where `L` is in meter. A magnetic field `B = B_(0)(hat(i) + hat(k))T` is present in the region. The flux passing through the loop `ABCDEFA` (in that order) is

Options

A. `B_0L^2Wb`
B. `2B_0L^2Wb`
C. `sqrt2B_0L^2Wb`
D. `sqrt4B_0L^2Wb`

Answer

B

Explanation

`phi=B.A`
`A=A_1+A_2=(L^2hatk+L^2hati)`
and `B=B_0(hati+hatk)T`
Now, `phi =B.A=B_0(hati+hatk)`.`(L^2hatk+L^2hati)`
`=2B_0L^2Wnb`