Facilitation_5_Tufts_SP25

Coulomb's Law Overview

• Explores the interactions between charged bodies.

• Key historical figure: Charles-Augustin de Coulomb, known for his pioneering work in electrostatics.

• Modern experiments continue to investigate similar principles.

Charge Arrangement and Forces

• Coulomb's Law in Practice:

  • Placed minimum 2 charges, q, at corners of a square.

  • The force experienced by these charges can be resolved into components.

  • Charges cancel each other out in the x-component, leading to a resultant positive y-component from a third charge (3q).

  • Resulting force in the y-direction (Fy) is positive, indicating a net upward force.

Electric Force Between Charges

• Two Charged Bodies at Square Vertices:

  • Two cases discussed: Case (a) with charge Q and Case (b) with charge 2Q.

  • Forces between the charges are equal but differ in strength due to distance.

  • The stronger force is noted in Case (a) due to shorter distance and higher numerator in the force equation.

• Force Calculation:

  • The general formula given for electric force:

    [ F = k \frac{Q_1 Q_2}{R^2} ]

  • Variables:

    • k: Coulomb's constant

    • Q1, Q2: magnitudes of the charges

    • R: distance between charges

Electric Forces in Triangular Configurations

• Three Point Charges:

  • Arrangement in an equilateral triangle creates unique electric forces.

  • Charges experience both repulsive and attractive forces:

    • Repulsive forces between like charges (e.g., +2Q) push away.

    • Attractive forces from opposite charges (e.g., -Q) pull together.

  • Forces need to be evaluated based on vector components.

  • Potential methods to calculate net force:

    • Intuitive elimination of options.

    • Algebraic calculations utilizing geometry of arrangement.

Net Force on Charges

• Finding Points of No Net Force:

  • Determine positions in a setup where an electron would experience zero force.

  • Considerations:

    • Forces are repulsive and depend on charge magnitudes and distance.

    • Incorrect assumptions can lead to miscalculations about force direction.

Force Changes with Charge Variation

• Effect of Charge Variation:

  • If charge B is quadrupled to 4Q while A remains unchanged:

  • Resulting force increases, summarized in equations showing force relationship:

  • New force magnitude referenced and compared to original force.

• Conclusively states relationship in terms of original force (F):

  • Net force changes as per Coulomb's law adjustments.

Equilibrium in Charged Systems

• Equilibrium Conditions:

  • System of charged spheres achieves equilibrium in a square formation.

  • Each charge interacts through springs (natural relaxed length being L/2).

  • Key calculations involve:

    • Spring constant k

    • Charge magnitudes affecting net forces in the configuration.

  • Use of Coulomb's law to determine net forces acting on individual charges.