Question:
The electric potential at a distance $r$ from a point charge $q$ is proportional to
The electric potential at a distance $r$ from a point charge $q$ is proportional to
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Remember that the electric potential due to a point charge decreases as you move away from it in an inverse relationship with the distance.
Updated On: May 31, 2026
- $1/r$
- $1/r^2$
- $r$
- $r^2$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The electric potential \( V \) at a distance \( r \) from a point charge \( q \) is given by the formula: \[V = k \frac{q}{r}\] where \( k \) is Coulomb's constant.
Step 2: Meaning
This equation tells us that the electric potential decreases as the inverse of the distance from the point charge. The proportionality to \( 1/r \) indicates how the potential changes with distance.
Step 3: Analysis
To understand why the correct answer is A, we need to analyze the relationship between the electric potential and the distance from a point charge: If we double the distance from the charge (i.e., change \( r \) to \( 2r \)), the new potential will be \( V' = k \frac{q}{2r} = \frac{1}{2} \left( k \frac{q}{r} \right) \). This shows that doubling the distance halves the potential, which is consistent with a proportionality to \( 1/r \). Option B suggests a proportionality to \( 1/r^2 \), which would mean that quadrupling the distance (i.e., changing \( r \) to \( 4r \)) would reduce the potential by a factor of four. This is not consistent with the inverse relationship observed in the formula for electric potential. Option C suggests a proportionality to \( r \). If this were true, increasing the distance from the charge would increase the potential linearly, which contradicts the known behavior of electric fields and potentials. Option D suggests a proportionality to \( r^2 \), which would imply that doubling the distance would quadruple the potential. This is also inconsistent with the inverse relationship observed in the formula for electric potential.
Step 4: Conclusion
The correct answer is A because the electric potential at a distance from a point charge is inversely proportional to the distance, following the formula \( V = k \frac{q}{r} \). Final Answer: (A)
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