A loop made of straight edegs 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_(0)L^(2)Wb`
B. `2B_(0)L^(2)Wb`
C. `sqrt2B_(0)L^(2)Wb`
D. `4B_(0)L^(2)Wb`

Answer

B

Explanation

Here, loop ABCDA lies in XY-plane whose area vector `A_(1)=L^(2)hatk`, whereas loop ADEFA lies in YZ-plane whose area vector `A_(2)=L^(2)hat"I"`.
Also, the magnetic flux linked with uniform surface of area A in uniform magnetic field is given by
`phi=B.A`

`A=A_(1)+A_(2)=(L^(2)hatk+L^(2)hat"i")`
and `B=B_(0)(hat"i"+hatk)T`
Now, `phi=B.A=B_(0)(hat"i"+hatk).(L^(2)hatk+L^(2)hat"i")=2B_(0)L^(2)Wb`