Question

The total flux associated with given cube will be, where ${}^{\prime }{a}^{\prime }$ is side of cube :–
$(\frac{1}{{ϵ}_o}=4\pi \times 9\times {10}^9)$

• A. $162\pi \times {10}^{-3}\frac{{\text{Nm}}^2}{\text{C}}$
  
• B. $162\pi \times {10}^3\frac{{\text{Nm}}^2}{\text{C}}$
  
• C. $162\pi \times {10}^{-6}\frac{{\text{Nm}}^2}{\text{C}}$
  
• D. $162\pi \times {10}^6\frac{{\text{Nm}}^2}{\text{C}}$
  

Answer 1

The correct option is B $162\pi \times {10}^3\frac{{\text{Nm}}^2}{\text{C}}$



Total flux through the cube due to any one charge is${\frac{1}{8}}^{th}$ of the total flux generated, as it can be imagined that the charge is at the centre of the bigger cube of which this cube is ${\frac{1}{8}}^{th}$ part.
So, ${\varphi }_{total}=\frac{1}{8}\frac{(1+2+3+4+5+6+7+8)}{{ϵ}_o}\mu C$
$=162\pi \times {10}^3\frac{{\text{Nm}}^2}{\text{C}}$