Question

A charge q is placed at one corner of a cube. The electric flux through any of the three faces adjacent to the charge is zero. The flux through any one of the other three faces is.

• A. $q/3{ϵ}_0$
• B. $q/6{ϵ}_0$
• C. $q/12{ϵ}_0$
• D. $q/24{ϵ}_0$

Answer 1

The correct option is D $q/24{ϵ}_0$

ACCORDING TO THE GIVEN PROBLEM, THE CHARGE IS PLACED AT THE CORNER OF THE CUBE AS SHOWN IN FIGHURE_1,

NOW CONSIDER THE ANOTHER FIGURE_2 IN WHICH THE WHOLE CHARGE IS ENCLOSED IN THE FOUR SUCH CUBE,

NOW CALCULATING THE FLUX THROUGH THE ALL CUBES AS TOTAL:

${\varphi }_e=\frac{q}{{ϵ}_0}=EA$

WHERE $A=6\ast (2a{)}^2$

FOR ONLY ONE SIDE OF FIRST CUBE,

AREA WILL BE $A_0=a^2$

FROM ABOVE DATA FLUX THROW THE SINGLE FACE (AREA = $A_0$ ) IS GIVEN BY:

${\varphi }_e=\frac{Q}{{ϵ}_0}=E{A}_0$

WHERE $Q=\frac{q}{24}$

SO THE FLUX THROUGH THROUGH THE SINGLE FACE IS $\frac{q}{24{ϵ}_0}$ ;

HENCDE THE OPTION (D) IS CORRECT.