COMEDK 2023 Shift 1 Paper

The electric flux (Φ) through a closed surface, such as the surface of a cube, is directly proportional to the charge enclosed (Q) by that surface. This relationship is dictated by Gauss's Law, which is represented by the equation:
Φ=‌

Q

ε0

where:
Φ is the electric flux,
Q is the charge enclosed by the surface,
ε0 is the permittivity of free space (a constant).
In the given problem,
The initial flux from a cube of side 1m is Φ.
When the side of the cube is increased to 3m, and the charge enclosed is reduced to a third of its original value (Q′=‌

Q

3

.) the relationship above can be used to find the new flux (Φ′).
Using the relation for electric flux and substituting the new charge value, we get:
Φ′=‌

Q′

ε0

=‌

‌ Q 3

ε0

=‌

1

3

⋅‌

Q

ε0

Since the original flux Φ=‌

Q

ε0

, substituting this back into the equation for Φ′ yields:
Φ′=‌

1

3

⋅Φ
Thus, the electric flux from the larger cube with side 3m and one third the original enclosed charge is ‌

Φ

3

. Therefore, the correct answer is:
Option A: ‌

Φ

3