Physics Electrostatics Potential & Capacitance Electric Potential and Potential Difference Single Correct MCQ
Published on: September 12, 2026

The electric potential outside a uniformly charged sphere at a distance ‘r’ is (‘a’ being the radius of the sphere)-

A
directly proportional to a 3
B
directly proportional to r.
C
inversely proportional to r.
D
inversely proportional to a 3 .

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Text Solution

Verified by Experts
The correct answer is:
B
Step 1: For a uniformly charged sphere, the electric potential outside the sphere behaves similarly to a point charge located at the center of the sphere. The electric potential at a distance 'r' from such a charge is given by the formula:
$$ V = \frac{kQ}{r} $$
where V is the electric potential, k is Coulomb's constant, Q is the total charge, and r is the distance from the center of the sphere.

Step 2: Since we are concerned with the potential outside the sphere, as distance 'r' increases, the influence of the charges effectively 'acts' like a point charge at the center.

Step 3: Therefore, the potential is directly dependent on the radial distance 'r', which confirms that it is directly proportional to 'r'.

Step 4: The radius 'a' of the sphere does not factor into the equation for electric potential outside the sphere, it only relates to the distribution of the charge.

Therefore the correct answer is: B.

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