A point charge of 9.00 ×10^-9 C is located at the origin of a coordinate system. A positive char

step 1 The first charge over there is a place on origin and one charge bring from to some point and the

A point charge of 9.00 ×10^-9 C is located at the origin of...

A point charge of $9.00 \times 10^{-9} \mathrm{C}$ is located at the origin of a coordinate system. A positive charge of $3.00 \times 10^{-9} \mathrm{C}$ is brought in from infinity to a point such'that the clectrical potential energy associated with the two charges is $8.09 \times 10^{-7}$ J. How far apart are the charges at this time? (See Sample Problem 18A.)

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Key Concepts

Electrostatic Potential Energy

Electrostatic potential energy is the energy stored due to the positions of charged objects. In a system of two point charges, this energy is given by the equation U = k(q1q2/r), where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between them. This concept is central to understanding how charges interact and how work is involved in assembling charge configurations.

Coulomb’s Law

Coulomb’s Law describes how the electrostatic force between two point charges depends on the magnitude of the charges and the distance between them. Specifically, it states that the force is directly proportional to the product of the charges and inversely proportional to the square of the separation. This law underpins the calculation of both the force and potential energy in systems of point charges.

Point Charge

A point charge is an idealized model in which the charged object is assumed to have negligible size compared to the distances involved in the problem. This simplification allows for the application of Coulomb’s Law and the derivation of formulas for electric potential and potential energy without considering the detailed structure or distribution of the charge.

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