Question

A loop made of straight edges has six corners at A(0, 0, 0), B(L, 0, 0), c(L, L, 0), D(0, L, 0), E(0, L, L) And F (0, 0, L). A magnetic field $\overline{B}=B_0(\hat{i}+\hat{k})T$ is present in the region.The flux passing through the loop ABCDEFA (in the order ) is

• A. $B_0{L}^{2}Wb$
• B. $2B_0{L}^{2}Wb$
• C. $\sqrt{2}{B}_0{L}^{2}Wb$
• D. $4B_0{L}^{2}Wb$

Answer 1

The correct option is B $2B_0{L}^{2}Wb$

Here, $\overline{B}=B_0(\hat{i}+\hat{k})T$
Area vector of ABCD = $L^2\hat{k}$
Area vector of DEFA = $L^2\hat{i}$
Total area vector, $\overline{A}=L^2\left(\hat{i}\hat{k}\right)$
Total magnetic flux, $\varphi =\overline{B}\cdot \overline{A}$
$=B_0(\hat{i}+\hat{k})\cdot L^2(\hat{i}\hat{k}=B_0{L}^2(1+1)=2B_0{L}^{2}Wb$