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Class 12 › Physics › Moving Charges and Magnetism
CBSE2023Class Class 12 · Physics1 Marks · Mcq✅ Verified
A square loop of side $L$ lies in the x-y plane in a magnetic field $\vec{B}=B_0(2\hat{i}+3\hat{j}+4\hat{k})$, where $B_0$ is a constant. The magnetic flux through the loop is:
A. $\sqrt{29}\,B_0L^2$
B. $4B_0L^2$
C. $3B_0L^2$
D. $2B_0L^2$
✅ Answer & Solution
✅ Correct Answer: B
The loop lies in the x-y plane, so its area vector is along the z-direction: $$\vec{A} = L^2\,\hat{k}$$ Magnetic flux: $$\phi = \vec{B}\cdot\vec{A} = B_0(2\hat{i}+3\hat{j}+4\hat{k})\cdot(L^2\hat{k})$$ Only the $\hat{k}$ component contributes: $$\phi = B_0(4)(L^2) = 4B_0L^2$$ Hence the correct option is (B).
