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

Also, the magnetic flux linked with uniform surface of area A in uniform magnetic field is given by
`varphi=B.A`
`A=A_(1)+A_(2)=(L^(2)hatk+L^(2)hati)`
and `B=B_(0)(hati+hatk)T`
Now, `varphi=B.A=B_(0)(hati+hatk)*(L^(2)hatk+L^(2)hati)`
= `2B_(0)L^(2)Wb`.