What is r in the formula U = ke(q1q2)/r?

Question

BlackTom AI · Accepted Answer

Here is how to dissect each option step by step and understand what r represents in the formula U = k_e (q1 q2)/r.

Option a: The distance between two charges. This is the correct interpretation. In the electrostatic potential energy formula for two point charges, r denotes the separation distance between the charges q1 and q2. The energy U scales inversely with r: as the charges move farther apart, U decreases, and as they come closer, U increases, assuming signs of charges are considered in the product q1 q2. The constant k_e sets the units and encloses Coulomb's constant.

Option b: The radius of the charge that contributes to the electric potential energy to be calculated. This is inaccurate for point-charge energy formulas. The expression U = k_e (q1 q2)/r assumes point charges with negligible spatial extent, and r is not a radius of a charge but a separation distance between their centers. Introducing a charge radius would complicate the model and is not what this formula uses.

Option c: The radial quantity of the electric potential energy in an electric charge inside an electric field. This statement confuses potential energy with potential energy density or with the concept of potential at a point. In this two-charge energy formula, r is not a radial coordinate of a single charge's energy content inside a field; it is simply the separation between the charges that determines the energy, not a property of a single charge's radial position within a field.

Option d: The rotational velocity of the moving charge which causes an electric potential energy. This describes angular or magnetic-type considerations and kinetic effects, not the static Coulomb potential energy between point charges. The given formula does not involve velocity; it is a static energy depending on charge magnitudes and their separation, so rotational or kinetic terms are not part of r here.

In summary, each distractor either misidentifies r as a property of a single charge (radius, velocity) or as a field-related radial quantity of a single charge, whereas the fundamental definition in this formula is that r is the distance between the two charges whose interaction energy is being calculated. The inverse dependence on r is a hallmark of Coulomb’s law, reinforcing that r is the inter-charge separation rather than any intrinsic radius or dynamical variable.

UCIC 202503 PHYS101 Quiz 9

What is r in the formula U = ke(q1q2)/r?

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