Question

A point charge ‘$q$’ is placed at the corner of a cube of side ‘$a$’ as shown in the figure. What is the electric flux through the face $ABCD$ ?

• A. $0$
• B. $\frac {q}{24\epsilon_o}$
• C. $\frac {q}{6\epsilon_o}$
• D. $\frac {q}{72\epsilon_o}$

Answer 1

Answer: (B)

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:
$
\phi_{ e }=\frac{ q }{\epsilon_{0}}= EA
$
WHERE A $=6 *(2 a)^{2}$
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:
$
\phi_{ e }=\frac{ Q }{\epsilon_{0}}= EA _{0}
$
WHERE Q $=\frac{q}{24}$
SO THE FLUX THROUGH THROUGH THE SINGLE FACE IS $\frac{ q }{24 \epsilon_{0}}$;