A loop ABCDEFA of straight edges has six corner points A(0, 0, 0), B(5, 0, 0), C(5, 5, 0), D (0, 5, 0), E(0, 5, 5) and F(0, 0, 5). The magnetic field in this region is \( \overrightarrow B = \left( {3\widehat i + 4\widehat k} \right)T \) . The quantity of flux through the loop ABCDEFA (in Wb) is _______.
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Correct Answer: 175
Solution and Explanation
Face ABCD (counter-clockwise seen from +z): \(\vec A_1=25\,\hat k\ \text{m}^2\).
Face ADEF (A(0,0,0), D(0,5,0), E(0,5,5), F(0,0,5), counter-clockwise seen from +x): \(\vec A_2=25\,\hat i\ \text{m}^2\).
\(\vec A=25(\hat i+\hat k)\). Flux \(\phi=\vec B\cdot\vec A=(3\hat i+4\hat k)\cdot25(\hat i+\hat k)=25(3+4)=175\) Wb.
Answer: 175
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