A loop $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}\mathrm{E}\mathrm{F}\mathrm{A}$ of straight edges has six corner points $A\left(0,0,0\right),B\left(5,0,0\right),C\left(5,5,0\right),D\left(0,5,0\right),E\left(0,5,5\right)$ and $F\left(0,0,5\right)$ . 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 $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}\mathrm{E}\mathrm{F}\mathrm{A}$ (in $\mathrm{W}\mathrm{b}$ ) is _____________

Solution

$\varphi =\overrightarrow{B}.\overrightarrow{A}=\left(3\widehat{i}+4\widehat{k}\right).\left(25\widehat{i}+25\widehat{k}\right)$

$\varphi =\left(2\times 25\right)+\left(4\times 25\right)=175\mathrm{w}\mathrm{e}\mathrm{b}\mathrm{e}\mathrm{r}$

Hence, the correct answer is 175.