• # question_answer A long string with a charge A per unit length passes through an imaginary cube of edge a. The maximum flux of the electric field through the cube will be A) $\frac{\lambda a}{{{\varepsilon }_{0}}}$                           B) $\frac{\sqrt{2}\lambda a}{{{\varepsilon }_{0}}}$  C)   $\frac{6\lambda {{a}^{2}}}{{{\varepsilon }_{0}}}$       D)   $\frac{\sqrt{3}\lambda a}{{{\varepsilon }_{0}}}$

The maximum length of the string which can be fit into the cube is equal to the body diagonal. We know that body diagonal of a cube is $\sqrt{3}\,a.$ The total charge inside the cube will be $(\sqrt{3}a)\times \lambda .$ According to Gauss's law, the total flux through the cube $\Phi =\frac{\text{Total}\,\text{Charge}}{{{\varepsilon }_{0}}}=\frac{\sqrt{3}a\lambda }{{{\varepsilon }_{0}}}$ Hence, the correction option is (d).