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Science
PhysicsPhysics for Scientists and Engineers: Foundations and Connections1st Edition
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A In Chapter 23, you will encounter the electric force that exists between two electrically charged objects, given by the formula F E = kq 1 q 2 / r 2 , where k is a constant called Coulomb’s constant, each q represents the amount of excess charge on each object, and r is the distance between the objects. Find the change in electric potential energy between two charges that are initially a distance r 1 apart and later a distance r 2 apart.

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Physics for Scientists and Enginee...

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Publisher: Cengage Learning
ISBN: 9781133939146
Chapter 8, Problem 66PQ
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A In Chapter 23, you will encounter the electric force that exists between two electrically charged objects, given by the formula FE = kq1q2/r2, where k is a constant called Coulomb’s constant, each q represents the amount of excess charge on each object, and r is the distance between the objects. Find the change in electric potential energy between two charges that are initially a distance r1 apart and later a distance r2 apart.

To determine

The change in electrical potential energy between two charges that are initially a distance r1 apart and later a distance r2 apart.

Explanation of Solution

Write the integral formula for change in electrical potential energy.

  ΔU=−∫rirfFEdr (I)

Here, ΔU is the change in electrical potential energy, ri is the initial distance of separation between the charges, ff is the final distance of separation between the charges, FE is the Coulomb force between the charges.

Write the expression for the Coulomb force between two charges.

  FE=kq1q2r2 (II)

Here, q1, and q2 are the charges, r is the distance of separation between the charges, and k is a constant (k=1/4πε0, where ε0 is the permittivity of free-space).

Use equation (II) in (I) and perform the integration

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