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. `sqrt2 B_(0) L^(2) Wb`
D. `4 B_(0) L^(2) Wb`

Answer

B

Explanation

Here, `vec B = B_(0) (hati + hatk)` , Refer to Fig.
Area vector of ABCD ` = L^(2) hat k`
Area vector of DEFA ` = L^(2) hat i`
Total area vector, `vec A = L^(2) (hati + hatk)`
Total magnetic flux,`phi = vec B .vec A = B_(0) (hati + hatk). L^(2) (hati + hatk) = B_(0) L^(2) (1 + 1) = 2 B_(0) L^(2) Wb`.