91影视

1. Magnetic flux through each of five faces of a die is${蠁}_b=卤NWb$.
2. For even N, flux is positive (outward).
3. For oddN, the flux is negative (inward).

Using Gauss law, write an expression for net magnetic flux through the die. Inserting the magnetic flux through five faces in it gives magnetic flux through the sixth face of the die.

The dice with 6 sides forms a closed Gaussian surface. Using Gauss law for magnetism, the net magnetic flux through any closed surface is zero.

${蠁}_b=鈭�B.dA=0............................\left(1\right)$

For 6 faces of the die,

$$\begin{gathered} {蠁}_b=\underset{N=1}{\overset{6}{鈭�}}{蠁}_{bN}=0 \\ {蠁}_{b1}+{蠁}_{b2}+{蠁}_{b3}+{蠁}_{b4}+{蠁}_{b5}+{蠁}_{b6}=0. \end{gathered}$$

It is given that for odd N, flux is negative and for even N, flux is positive.

$\begin{array}{rcl}-1Wb+2Wb-3Wb+4Wb-5Wb+{蠁}_{b6}& =& 0\\ -9Wb+6Wb+{蠁}_{b6}& =& 0\\ {蠁}_{b6}& =& -3Wb\end{array}$

Hence, the magnetic flux through the sixth face is - 3 Wb.