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. $\frac{q}{24{ϵ}_o}$
• C. $\frac{q}{6{ϵ}_o}$
• D. $\frac{q}{72{ϵ}_o}$

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:
$<br/>{\varphi }_e=\frac{q}{{ϵ}_0}=EA<br/>$
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:
$<br/>{\varphi }_e=\frac{Q}{{ϵ}_0}=E{A}_0<br/>$
WHERE Q $=\frac{q}{24}$
SO THE FLUX THROUGH THROUGH THE SINGLE FACE IS $\frac{q}{24{ϵ}_0}$;