AP®ChemistryCollege BoardStudy GuidesUnit 1: Atomic Structure & PropertiesAtoms & ElectronsUsing Coulomb’s Law

Using Coulomb’s Law (College Board AP® Chemistry)

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Reviewed by: Stewart Hird

Using Coulomb’s Law

  • Coulomb's law describes the electrostatic force between two charged particles

  • It states that the force is directly proportional to the product of their charges and inversely proportional to the square of the distance between them

    • straight F subscript coulombic space straight alpha space left parenthesis straight q subscript 1 cross times straight q subscript 2 right parenthesis

    • straight F subscript coulombic space straight alpha space 1 over straight r squared

  • The formula for Coulomb's law is straight F subscript coulombic space equals space straight k space fraction numerator straight q subscript 1 straight q subscript 2 over denominator straight r squared end fraction , where:

    • Fcoulombic is the force between the charges in Newtons (N)

    • k is Coulomb's constant (approximately 8.99 x 109 N·m² C-²)

    • q1 and q2 are the value of the charges in Coulombs (C), which is the unit of measurement for charge

    • r is the distance between the charges in meters (m)

  • The force is attractive for opposite charges and repulsive for like charges

Examiner Tips and Tricks

Always verify the units before any calculation. If the units are not consistent, make sure to perform any transformation before replacing the values into the Coulomb's Law formula

Worked Example

Calculating the force that exists between a proton and an electron given the following information.

Charge of a proton = +1.602 x 10-19 C
Charge of an electron = -1.602 x 10-19 C
Distance between them = 1 x 10-10 m

Answer:

  • Step 1: Write down the values and the Coulomb's law formula

q1 = +1.602 x 10-19 C

q2 = -1.602 x 10-19 C

r = 1 x 10-10 m

k = 8.99 x 109 N·m² C-²

 Error converting from MathML to accessible text.

  • Step 2: Replace the value in the Coulomb’s Law

 Error converting from MathML to accessible text.

straight F subscript coulombic space equals 8.99 space cross times space 10 to the power of 9 space straight N space straight m ² straight C to the power of negative 2 end exponent space space fraction numerator left parenthesis plus 1.602 cross times 10 to the power of negative 19 end exponent space straight C right parenthesis left parenthesis negative 1.602 cross times 10 to the power of negative 19 end exponent space straight C right parenthesis over denominator left parenthesis 1 cross times 10 to the power of negative 10 end exponent space straight m right parenthesis squared end fraction

  • Step 3: Calculate the force.

Fcoulombic = -2.31 x 10-8 N

  • The negative sign indicates an attractive force since proton and electron have opposite charges

Examiner Tips and Tricks

If the problem does not state the charge of the electron, you can find it in the AP Chemistry Equations and Constants that appear at the beginning of your examination. The charge of the proton has the same value but with a positive sign

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    Martín

    Author: Martín

    Expertise: Chemistry Content Creator

    Martín, a dedicated chemistry teacher and tutor, excels in guiding students through IB, AP, and IGCSE Chemistry. As an IB Chemistry student, he came from hands-on preparation, focusing on practical exam techniques and rigorous practice. While at Universidad San Francisco de Quito, his academic journey sparked a passion for computational and physical chemistry. Martín specializes in chemistry, and he knows that SaveMyExams is the right place if he wants to have a positive impact all around the world.

    Stewart Hird

    Author: Stewart Hird

    Expertise: Chemistry Lead

    Stewart has been an enthusiastic GCSE, IGCSE, A Level and IB teacher for more than 30 years in the UK as well as overseas, and has also been an examiner for IB and A Level. As a long-standing Head of Science, Stewart brings a wealth of experience to creating Topic Questions and revision materials for Save My Exams. Stewart specialises in Chemistry, but has also taught Physics and Environmental Systems and Societies.