A battery of emf \[{{E}_{0}}=12\,V\] is connected across a 4 m long uniform wire having resistance \[\frac{4\Omega }{m}\] the cells of small m emfs \[{{\varepsilon }_{1}}=2\,V\] and \[{{\varepsilon }_{2}}=4\,V\] having internal resistance 2\[\Omega \] and 6\[\Omega \] respectively, are connected as shown in the figure. If galvanometer shows no deflection at the point N, the distance of point N from the point A is equal to

• A. \[\frac{1}{6}m\]                        
• B. \[\frac{1}{3}m\]
• C. \[25m\] 
• D. \[50m\]