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 $\vec{B}=B_0(\hat{i}+\hat{k})T$ is present in the region. The flux passing through the loop $ABCDEFA$ (in that 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

Answer: (B)

Here, $\vec{B}=B_0(\hat{i}+\hat{k})T$

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