Weeks 2 and 3 - Electric charge and Electric field

Lectures I and II: Overview

  • Topics Covered: Electric charge, force, electric field, applications

Electric Charge

  • Definition: An intrinsic property of particles that make up matter.

Nature of Electric Charge

  • Charge can be positive (+) or negative (-).

Composition of Atoms

  • Atoms consist of:

    • Electrons: Negatively charged

    • Protons: Positively charged

    • Neutrons: No charge

Measurement of Charge

  • Unit: Coulombs (C)

  • Elementary charge:

    • Charge of the proton = +1.6 x 10^-19 C

    • Charge of the electron = -1.6 x 10^-19 C

  • Protons and neutrons are made of quarks, which have fractional charges (2/3 and -1/3).

Conservation of Charge

  • Charge cannot be created or destroyed, only moved.

  • Charges experience electrostatic forces:

    • Like charges repel each other.

    • Opposite charges attract each other.

Example: Balloon and Hair Experiment

  • Rubbing a balloon on hair transfers electrons.

    • Balloon: Negatively charged

    • Hair: Positively charged

  • Results in attraction between the balloon and hair.

  • Movement towards walls can also induce charge changes on surfaces.

Coulomb's Force Law

  • Defines electric force between two charges:

    • Formula:[ F = k \frac{|q_1 \cdot q_2|}{r^2} ]

    • Where:

    • ( F ): electrostatic force

    • ( k ): Coulomb's constant = 9 x 10^9 N m²/C²

    • ( q_1, q_2 ): magnitudes of the charges

    • ( r ): distance between the charges

Electrostatic Force

  • Nature: Vector quantity having magnitude and direction.

  • Magnitude is calculated using:[ |F| = \sqrt{F_x^2 + F_y^2 + F_z^2} ]

Example Calculation

  • Two 0.5 kg spheres, charged at 100 μC, 25 cm apart:

    • Calculate force and compare to weight.

Principle of Superposition

  • When multiple charges are present, the total force on a charge is the vector sum of forces from all other charges.

Electric Field

  • Definition: The electric field at a point is the force a unit charge would experience at that point.

  • Direction depicted by electric field lines.

    • Lines originate from positive charges, terminate on negative charges.

    • Closer lines indicate stronger fields.

Calculation of Electric Field

  • Formula:[ E = \frac{F}{q} ]

    • Units: N/C

  • Field of a Positive Charge: Direction is outward from the charge.

  • Field of a Negative Charge: Direction is inward toward the charge.

Examples

  • Calculate electric fields and forces acting on charges positioned in fields:

    • Example involving +5.0 mC and -2.0 mC charges, demonstrating superposition principles.

Electric Dipole

  • Formation: A pair of positive and negative charges.

  • Example: Water (H2O) molecule.

  • Behavior in electric fields: Experiences torque but no net force.

Conductors and Insulators

  • Conductors:

    • Metals (e.g. copper, iron) have freely moving electrons allowing electric current flow.

  • Insulators:

    • Non-metals (e.g. glass, rubber) have tightly held electrons, preventing current flow.

  • Semiconductors:

    • Materials like silicon have properties between conductors and insulators.

Summary

  • Matter consists of positive and negative charges (electrons/protons carry an elementary charge of 1.6 x 10^-19 C).

  • Electrostatic forces are described by Coulomb's Law, summing as vectors in the presence of multiple charges.

  • The electric field characterizes the force field surrounding charges and influences behavior.