Question

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). A magnetic field `B = B_o(hati + hatk)`T is present in the region. The flux passing through the loop ABCDEFA (in that order) is ______.

Options

• `B_o L^2  Wb`

• `2B_o L^2  Wb`

• `sqrt(2) B_o L^2  Wb`

• `4B_o L^2  Wb`

Answer 1

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). A magnetic field `B = B_o(hati + hatk)`T is present in the region. The flux passing through the loop ABCDEFA (in that order) is `underline(2B_o L^2  Wb`).

Explanation:

In this problem first we have to analyse area vector, loop ABCDA lies in x-y  plane whose area vector `vecA_1 = L^2  hatk` whereas loop ADEFA lies in y-z plane whose area vector `vecA_2 = L^2 hati`

And the magnetic flux is `phi_m = vecB * vecA`

`vecA = vecA_1 + vecA_2 = (L^2  hatk + L^2 hati)`

And `vecB = B_0(hati + hatk)`

Now, `phi_m = vecB * vecA = B_0(hati + hatk)*(L^2  hatk + L^2hati)`

= `2B_0L^2  Wb`