Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Gauss’s law is true only if force due to a charge varies as
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Analyze Gauss's Law, which states that the electric flux through a closed surface is proportional to the charge enclosed by that surface. The mathematical expression is given by:
$$ \Phi_E = \frac{Q_{enc}}{\epsilon_0} $$
where \( \Phi_E \) is the electric flux, \( Q_{enc} \) is the enclosed charge, and \( \epsilon_0 \) is the permittivity of free space.
Step 2: Recognize that for the law to hold true, the electric field generated by a point charge must vary as \( \frac{1}{r^2} \), where \( r \) is the distance from the charge. This corresponds with Option A, which is commonly depicted as the expression: \( F \propto \frac{1}{r^2} \). Hence, the electric field direction is radially outwards from a point charge and the law is applicable to symmetrical configurations (point, spherical).
Therefore, the correct answer is A.
$$ \Phi_E = \frac{Q_{enc}}{\epsilon_0} $$
where \( \Phi_E \) is the electric flux, \( Q_{enc} \) is the enclosed charge, and \( \epsilon_0 \) is the permittivity of free space.
Step 2: Recognize that for the law to hold true, the electric field generated by a point charge must vary as \( \frac{1}{r^2} \), where \( r \) is the distance from the charge. This corresponds with Option A, which is commonly depicted as the expression: \( F \propto \frac{1}{r^2} \). Hence, the electric field direction is radially outwards from a point charge and the law is applicable to symmetrical configurations (point, spherical).
Therefore, the correct answer is A.
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