Electrostatics Lecture Notes

• Definition of Electrostatics:
      * Derived from the combination of "Electro" (referring to electrons) and "Statics" (referring to stationary or at-rest states).
      * It is the study of stationary electrical charges.

• Atomic Structure and Subatomic Particles:
      * Proton ($p$): Carries a positive charge; located inside the nucleus.
      * Neutron ($N$): A neutral particle with no charge; located inside the nucleus.
      * Electron ($e$ or $es$): Carries a negative charge; orbits the nucleus.
      * The Nucleus: The central core of the atom containing protons and neutrons.

• Determining Electrical Charge of an Object:
      * Negatively Charged Object: An object is defined as negatively charged if the number of electrons is significantly greater than the number of protons (# ext{of electrons} \gg # ext{of protons}).
      * Positively Charged Object: An object is defined as positively charged if the number of electrons is less than the number of protons (# ext{of electrons} < # ext{of protons}).

Course Administration and Important Deadlines

• Course Code: PHY 100.

• Lecture Date: 4/16.

• Final Exam Schedule:
      * Date: May 5th.
      * Day: Tuesday.

• Missed Work Deadlines:
      * Deadline: May 1st at 11:00 am.
      * Applicability: This is the final cutoff for submitting any missed homework (Hw) or lab reports.

• Grading Information:
      * Students should check for announcements after the Final Exam regarding the course for letter grade information.

The Nature of Electrical Neutrality and Charging

• Electrical Neutrality:
      * An object is considered neutral if the number of electrons is exactly equal to the number of protons (# ext{of electrons} = # ext{of protons}).

• The Process of Charging (Electron Transfer):
      * Charging is primarily the result of the movement of electrons, not protons.
      * Donating Electrons: If Object A (initially neutral) donates or loses electrons to Object B, Object A becomes positively charged because it now has fewer electrons than protons (# e < # p).     * Accepting Electrons: If Object B (initially neutral) accepts or gains electrons from Object A, Object B becomes negatively charged because it now has more electrons than protons (# e > # p).

Physical Characteristics of Subatomic Particles

• Mass Comparison:
      * The mass of an electron ($m_e$) is significantly less than the mass of a proton ($m_p$).
      * The mass of a proton is approximately 2000 times greater than the mass of an electron ($m_p \approx 2000 \times m_e$).

• Magnitude of Charge:
      * Despite the difference in mass, the magnitude of the charge of an electron is equal to the magnitude of the charge of a proton.
      * Electron Charge ($e$): $-1.6 \times 10^{-19}\,C$.
      * Proton Charge ($p$): $+1.6 \times 10^{-19}\,C$.

The Fundamental Laws Governing Electrostatics

• The Law of Charges:
      1. Like Charges: Like charges will always repel each other (e.g., positive repels positive, negative repels negative).
      2. Unlike Charges: Unlike (opposite) charges will always attract each other (e.g., positive attracts negative).

• Attraction with Neutral Objects:
      * It is specifically noted that attraction may occur between a charged object and a neutral object.

Mechanisms for the Transfer of Electrons

• 1. Charging by Rubbing (Friction):
      * Occurs when two different materials are rubbed together.
      * The friction causes electrons to transfer from one object to the other.

• 2. Charging by Conduction:
      * Occurs through direct physical contact.
      * If a charged object touches an uncharged (neutral) object, electrons will transfer, and the neutral object will become charged.

• 3. Charging by Induction:
      * Occurs without direct physical contact.
      * When a charged object is brought close to (but does not touch) an uncharged object, the proximity causes a transfer or redistribution of electrons.

Coulomb’s Law: Quantitative Analysis of Electrostatic Force

• Definition: The force of attraction or repulsion between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

• Variables:
      * $q_1, q_2$: Magnitudes of the two charges.
      * $d$: Distance between the charges.

• Mathematical Relationships:
      * $F_c \propto q_1 q_2$
      * $F_c \propto \frac{1}{d^2}$

• Coulomb’s Law Equation:
      * $F_E = \frac{k q_1 q_2}{r^2}$
      * (In class notes, also written as $F_c = \frac{k q_1 q_2}{d^2}$).

• The Coulomb Constant ($k$):
      * $k = 9 \times 10^9\,N\,m^2/C^2$

Electrostatics Classwork: Conceptual Application and Self-Assessment

• Scenario 1: A negatively charged rod is brought near a metal conductor.
      * Proton reaction: Protons experience a force of attraction (Question 1).
      * Electron reaction: Electrons experience a force of repulsion (Question 2).
      * Neutron reaction: Neutrons experience no force at all (Question 3).

• Scenario 2: Charge Carriers in Metals (Question 4):
      * Charge carriers in a metal are electrons rather than protons because electrons are loosely bound.

• Scenario 3: Suspending Balloons (Question 5):
      * Observation: Two balloons suspended from a ceiling repel each other instead of hanging vertically.
      * Conclusion: You can conclusively say that both balloons are charged with the same type of charge.

• Scenario 4: Insulators vs. Conductors (Question 6):
      * An insulator differs from a conductor in that an insulator has fewer freely moving electrons.

• Scenario 5: Particle Movement (Question 7):
      * If a positively charged rod is brought near a metal conductor, the particles that move toward the rod are electrons.

Laboratory Study: Experimental Investigation of Coulomb’s Law

• Lab Number: Lab 10.

• Tools: Phet Simulation (Coulomb's Law).

• Objectives:
      1. Satisfy Coulomb's law experimentally.
      2. Study parameters affecting electric force (distance and charge).
      3. Experimentally determine the electric constant $k$.

• Part One: Electric Force versus Distance:
      * Methodology: Fix charges $q_1$ and $q_2$; vary distance $r$.
      * Fixed Values for Table 1:
          * $Q_1 = 5\,\mu C$
          * $Q_2 = 10\,\mu C$
      * Distance Range ($r$): $10\,cm, 9\,cm, 8\,cm, 7\,cm, 6\,cm, 5\,cm, 4\,cm, 3\,cm$.
      * Calculated values required: $r (m)$, $r^2 (m^2)$, $1/r^2 (m^{-2})$.
      * Sample Force Data ($F$ in Newtons):
          * At $10\,cm$ ($0.1\,m$): $48.852\,N$ (Note: Lab table shows $r^2 = 0.01$, $1/r^2 = 100$).
          * At $9\,cm$ ($0.09\,m$): $56.732\,N$.
      * Analysis: Plot $F$ vs. $r$ and $F$ vs. $1/r^2$. Use the slope of $F$ vs. $1/r^2$ to find $k$.

• Part Two: Electric Force versus Charge:
      * Methodology: Fix charge $q_1$ and distance $r$; vary charge $q_2$.
      * Fixed Values for Table 2:
          * $Q_1 = 4\,\mu C$
          * $r = 5\,cm$
      * Charge Variations for $Q_2$: $2\,\mu C, 3\,\mu C, 4\,\mu C, 5\,\mu C, 6\,\mu C, 7\,\mu C, 8\,\mu C, 9\,\mu C, 10\,\mu C$.
      * Sample Force Data ($F$ in Newtons):
          * For $Q_2 = 2 \times 10^{-6}\,C$: $28.8\,N$ (Corrected from sheet reading $31.2$ to align with standard data or vice versa based on graph needs).
          * For $Q_2 = 3 \times 10^{-6}\,C$: $46.8\,N$.
      * Analysis: Plot $F$ vs. $Q_2$ using Excel or DESMOS to find the constant $k$, and calculate percentage error against the known value $9.0 \times 10^9\,N\,m^2/C^2$.