A) \[\frac{\lambda a}{{{\varepsilon }_{0}}}\]
B) \[\frac{\sqrt{2}\lambda a}{{{\varepsilon }_{0}}}\]
C) \[\frac{6\lambda {{a}^{2}}}{{{\varepsilon }_{0}}}\]
D) \[\frac{\sqrt{3}\lambda a}{{{\varepsilon }_{0}}}\]
Correct Answer: D
Solution :
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).
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