question_answer

A charged particle g is placed at the centre O of cube of length L (ABCDEFGH). Another same charge q is placed at a distance L from 0. Then, the electric flux through ABCD is [AIEEE 2002]

A) \[q/4\pi {{\varepsilon }_{0}}L\]

B) zero

C) \[q/2\pi {{\varepsilon }_{0}}L\]

D) None of these

Correct Answer: D

Solution :

(*) Electric flux for any closed surface is defined as\[\phi =\oint{E.\,ds}\]

The flux through ABCD can be calculated, by first taking a small elemental surface and then writing the E. ds for this element, keep in mind that electric field at the location of this element is the resultant of both the charges.

It is quite obvious the flux through ABCD comes out to be non-zero because at every point of the surface, the angle between E and ds is less than \[{{90}^{o}}\] giving a positive non-zero value for the entire surface. So, option [b] cannot be the answer.

The options [a], [c] and [d] are dimensionally incorrect, so they cannot be answer.