If the magnetic field \( \vec{B}=\hat{i}-0.3 \hat{j} \) and the area \( \vec{A}=\hat{i}+6 \hat{j}-3 \hat{k} \) then the magnetic flux through this area is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → -0.8 unit
The magnetic flux through an area is the scalar (dot) product of the field and the area vector, \( \phi_B = \vec{B}\cdot\vec{A} \). In a dot product only the components along the same axis multiply.
\( \phi_B = (\hat{i} - 0.3\hat{j})\cdot(\hat{i} + 6\hat{j} - 3\hat{k}) \)
\( \phi_B = (1)(1) + (-0.3)(6) + (0)(-3) \)
\( \phi_B = 1 - 1.8 + 0 = -0.8 \)