Coulomb's Law and Electric Charges

Electric Charges

  • Like charges repel, and opposite charges attract.

  • In ordinary matter, positive charge comes from protons, and negative charge from electrons.

  • Protons and electrons have a strong attractive force due to their opposite charges.

  • Electrons maintain separation from the nucleus due to their wavelike properties, requiring space.

  • Protons, despite repelling each other, are held together by strong nuclear forces.

Charge Model

SI Unit of Charge: Coulomb (C)

  • The Coulomb is the SI unit of electric charge.

  • One Coulomb is the amount of charge carried by a current of one ampere in one second.
    1 A = 1 \frac{C}{s}

Coulomb’s Law

  • Describes the attractive and repulsive forces between charges.

Coulomb's Constant and Electrical Permittivity

  • Coulomb's constant relates force to charge and distance.

Electrical permittivity of free space is denoted by \epsilon0: \epsilon0 = 8.85 \times 10^{-12} \frac{N \cdot m^2}{C^2}

Force Formula: \vec{F} = k \frac{q1 q2}{r^2} \hat{r} = \frac{1}{4 \pi \epsilon0} \frac{q1 q_2}{r^2} \hat{r}

Comparing Electrostatic and Gravitational Forces

  • Example question: What two equal and opposite charges produce an electrostatic attraction force of 10 N at a 1-m separation?

  • Example question: What two equal masses produce a gravitational attraction force of 10 N at a 1-m separation?

Elementary Charge

  • Smallest possible charges are those of the electron and proton.
    e = 1.6 \times 10^{-19} C

  • Calculation of the number of electrons in a coulomb:
    N \times 1.6 \times 10^{-19} = 1 C
    N = \frac{1}{1.6 \times 10^{-19}} = 6.25 \times 10^{18} \text{ electrons in 1 C}

  • e is the elementary unit of charge and a fundamental constant.

Examples

  • Two identical metal spheres A and B are in contact and initially neutral. \1.0 \times 10^{12} electrons are added to sphere A, then the two spheres are separated. Afterward, what are the charge of A and the charge of B?

  • Two 1.0 kg masses are 1.0 m apart on a frictionless table. Each has +1.0 μC of charge.

    • What is the magnitude of the electric force on one of the masses?

    • What is the initial acceleration of each mass if they are released and allowed to move?

  • What is the magnitude of the electric force between an iron nucleus and its innermost electron if the distance between them is 1.5 \times 10^{-12} m?

  • Older pennies are 3.1 g of solid copper. What are the total positive charge and total negative charge in a solid copper penny that is electrically neutral? The density of copper is 8900 kg/m³.

  • Objects A and B are both positively charged. Both have a mass of 100 g, but A has twice the charge of B. When A and B are placed with 10 cm between their centers, B experiences an electric force of 0.45 N.

    • How large is the force on A?

    • What are the charges of A and B?

  • What is the magnitude of the force on the 1.0 nC charge in the middle of Figure P20.49 due to the four other charges?

Electric Charge

  • The strength of a particle’s electrical interaction with objects depends on its electric charge (positive or negative).

Conductors and Insulators

  • Conductors have many electrons free to move.

  • Insulators (nonconductors) have charged particles that are not free to move.

Conservation of Charge

  • The net electric charge of any isolated system is always conserved.

Coulomb’s Law (Summary)

  • The magnitude of the electrical force between two charged particles is proportional to the product of their charges and inversely proportional to the square of their separation distance.

  • F= \frac{1}{4\pi\in_0}\frac{q_1q_2}{r^2}

The Elementary Charge

  • Electric charge is quantized (restricted to certain values).
    e = 1.602 \times 10^{-19} C