What is r in the formula V = ke q/r?

Question

BlackTom AI · Accepted Answer

Question: What is r in the formula V = k_e q / r?

Option a: The distance from a charge to a point where the electric potential is to be calculated
- This is correct. In the expression for electric potential due to a point charge, V = k_e q / r, r represents the straight-line distance between the charge and the point at which the potential is being evaluated. It is a spatial separation, not a property of the charge itself, and it determines how the potential diminishes with distance. The larger r is, the smaller the potential, consistent with the inverse relationship.

Option b: The radial quantity of the electric potential energy in an electric charge inside an electric field
- This is incorrect. Electric potential energy is a separate concept from electric potential. Potential energy depends on the configuration of charges and their distances, while V is the potential per unit charge (voltage) at a location and does not describe energy directly. Also, V is not the energy itself but the energy per unit charge, so describing r as a radial quantity of potential energy is a conceptual mix-up.

Option c: The rotational velocity of the moving charge which causes an electric potential
- This is incorrect. The formula V = k_e q / r does not involve rotational velocity or any motion attribute of the charge. It applies to a static point charge observation point. Introducing rotational velocity would imply a dynamic scenario with magnetic effects, which is not represented in the simple Coulombic potential formula.

Option d: The radius of the charge that contributes to the electric potential to be calculated
- This is incorrect. For a point charge, the radius is zero (and for a true mathematical point, r is the distance to the observation point, not the radius of a charge distribution). In the context of the formula, r is the distance from the charge to the point where you are calculating the potential, not some intrinsic radius of the charge itself. In extended charge distributions, r can still be the distance from the charge element to the observation point, but the statement here mischaracterizes r as a radius of the charge rather than a separation distance.

Summary: The only option that accurately defines r in V = k_e q / r is the distance from the charge to the point where the potential is being calculated, while all other options misinterpret r as energy, motion, or a charge radius.

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