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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`
Solution
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`
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