Table of contents
- 0. Math Review(0)
- 1. Intro to Physics Units(0)
- 2. 1D Motion / Kinematics(0)
- Vectors, Scalars, & Displacement(0)
- Average Velocity(0)
- Intro to Acceleration(0)
- Position-Time Graphs & Velocity(0)
- Conceptual Problems with Position-Time Graphs(0)
- Velocity-Time Graphs & Acceleration(0)
- Calculating Displacement from Velocity-Time Graphs(0)
- Conceptual Problems with Velocity-Time Graphs(0)
- Calculating Change in Velocity from Acceleration-Time Graphs(0)
- Graphing Position, Velocity, and Acceleration Graphs(0)
- Kinematics Equations(0)
- Vertical Motion and Free Fall(0)
- Catch/Overtake Problems(0)
- 3. Vectors(0)
- Review of Vectors vs. Scalars(0)
- Introduction to Vectors(0)
- Adding Vectors Graphically(0)
- Vector Composition & Decomposition(0)
- Adding Vectors by Components(0)
- Trig Review(0)
- Unit Vectors(0)
- Introduction to Dot Product (Scalar Product)(0)
- Calculating Dot Product Using Components(0)
- Intro to Cross Product (Vector Product)(0)
- Calculating Cross Product Using Components(0)
- 4. 2D Kinematics(0)
- 5. Projectile Motion(0)
- 6. Intro to Forces (Dynamics)(0)
- 7. Friction, Inclines, Systems(0)
- 8. Centripetal Forces & Gravitation(0)
- Uniform Circular Motion(0)
- Period and Frequency in Uniform Circular Motion(0)
- Centripetal Forces(0)
- Vertical Centripetal Forces(0)
- Flat Curves(0)
- Banked Curves(0)
- Newton's Law of Gravity(0)
- Gravitational Forces in 2D(0)
- Acceleration Due to Gravity(0)
- Satellite Motion: Intro(0)
- Satellite Motion: Speed & Period(0)
- Geosynchronous Orbits(0)
- Overview of Kepler's Laws(0)
- Kepler's First Law(0)
- Kepler's Third Law(0)
- Kepler's Third Law for Elliptical Orbits(0)
- Gravitational Potential Energy(0)
- Gravitational Potential Energy for Systems of Masses(0)
- Escape Velocity(0)
- Energy of Circular Orbits(0)
- Energy of Elliptical Orbits(0)
- Black Holes(0)
- Gravitational Force Inside the Earth(0)
- Mass Distribution with Calculus(0)
- 9. Work & Energy(0)
- 10. Conservation of Energy(0)
- Intro to Energy Types(0)
- Gravitational Potential Energy(0)
- Intro to Conservation of Energy(0)
- Energy with Non-Conservative Forces(0)
- Springs & Elastic Potential Energy(0)
- Solving Projectile Motion Using Energy(0)
- Motion Along Curved Paths(0)
- Rollercoaster Problems(0)
- Pendulum Problems(0)
- Energy in Connected Objects (Systems)(0)
- Force & Potential Energy(0)
- 11. Momentum & Impulse(0)
- Intro to Momentum(0)
- Intro to Impulse(0)
- Impulse with Variable Forces(0)
- Intro to Conservation of Momentum(0)
- Push-Away Problems(0)
- Types of Collisions(0)
- Completely Inelastic Collisions(0)
- Adding Mass to a Moving System(0)
- Collisions & Motion (Momentum & Energy)(0)
- Ballistic Pendulum(0)
- Collisions with Springs(0)
- Elastic Collisions(0)
- How to Identify the Type of Collision(0)
- Intro to Center of Mass(0)
- 12. Rotational Kinematics(0)
- 13. Rotational Inertia & Energy(0)
- More Conservation of Energy Problems(0)
- Conservation of Energy in Rolling Motion(0)
- Parallel Axis Theorem(0)
- Intro to Moment of Inertia(0)
- Moment of Inertia via Integration(0)
- Moment of Inertia of Systems(0)
- Moment of Inertia & Mass Distribution(0)
- Intro to Rotational Kinetic Energy(0)
- Energy of Rolling Motion(0)
- Types of Motion & Energy(0)
- Conservation of Energy with Rotation(0)
- Torque with Kinematic Equations(0)
- Rotational Dynamics with Two Motions(0)
- Rotational Dynamics of Rolling Motion(0)
- 14. Torque & Rotational Dynamics(0)
- 15. Rotational Equilibrium(0)
- 16. Angular Momentum(0)
- Opening/Closing Arms on Rotating Stool(0)
- Conservation of Angular Momentum(0)
- Angular Momentum & Newton's Second Law(0)
- Intro to Angular Collisions(0)
- Jumping Into/Out of Moving Disc(0)
- Spinning on String of Variable Length(0)
- Angular Collisions with Linear Motion(0)
- Intro to Angular Momentum(0)
- Angular Momentum of a Point Mass(0)
- Angular Momentum of Objects in Linear Motion(0)
- 17. Periodic Motion(0)
- 18. Waves & Sound(0)
- Intro to Waves(0)
- Velocity of Transverse Waves(0)
- Velocity of Longitudinal Waves(0)
- Wave Functions(0)
- Phase Constant(0)
- Average Power of Waves on Strings(0)
- Wave Intensity(0)
- Sound Intensity(0)
- Wave Interference(0)
- Superposition of Wave Functions(0)
- Standing Waves(0)
- Standing Wave Functions(0)
- Standing Sound Waves(0)
- Beats(0)
- The Doppler Effect(0)
- 19. Fluid Mechanics(0)
- 20. Heat and Temperature(0)
- Temperature(0)
- Linear Thermal Expansion(0)
- Volume Thermal Expansion(0)
- Moles and Avogadro's Number(0)
- Specific Heat & Temperature Changes(0)
- Latent Heat & Phase Changes(0)
- Intro to Calorimetry(0)
- Calorimetry with Temperature and Phase Changes(0)
- Advanced Calorimetry: Equilibrium Temperature with Phase Changes(0)
- Phase Diagrams, Triple Points and Critical Points(0)
- Heat Transfer(0)
- 21. Kinetic Theory of Ideal Gases(0)
- 22. The First Law of Thermodynamics(0)
- 23. The Second Law of Thermodynamics(0)
- 24. Electric Force & Field; Gauss' Law(0)
- 25. Electric Potential(0)
- 26. Capacitors & Dielectrics(0)
- 27. Resistors & DC Circuits(0)
- 28. Magnetic Fields and Forces(0)
- 29. Sources of Magnetic Field(0)
- Magnetic Field Produced by Moving Charges(0)
- Magnetic Field Produced by Straight Currents(0)
- Magnetic Force Between Parallel Currents(0)
- Magnetic Force Between Two Moving Charges(0)
- Magnetic Field Produced by Loops and Solenoids(0)
- Toroidal Solenoids aka Toroids(0)
- Biot-Savart Law (Calculus)(0)
- Ampere's Law (Calculus)(0)
- 30. Induction and Inductance(0)
- 31. Alternating Current(0)
- Alternating Voltages and Currents(0)
- RMS Current and Voltage(0)
- Phasors(0)
- Resistors in AC Circuits(0)
- Phasors for Resistors(0)
- Capacitors in AC Circuits(0)
- Phasors for Capacitors(0)
- Inductors in AC Circuits(0)
- Phasors for Inductors(0)
- Impedance in AC Circuits(0)
- Series LRC Circuits(0)
- Resonance in Series LRC Circuits(0)
- Power in AC Circuits(0)
- 32. Electromagnetic Waves(0)
- 33. Geometric Optics(0)
- 34. Wave Optics(0)
- 35. Special Relativity(0)
24. Electric Force & Field; Gauss' Law
Electric Charge
24. Electric Force & Field; Gauss' Law
Electric Charge: Study with Video Lessons, Practice Problems & Examples
12PRACTICE PROBLEM
A small charge with a mass "m" of 2.0 grams is attached to an insulating string that is 60 cm long. This setup is observed to be in equilibrium within a uniform horizontal electric field of 9600 N/C. The electric field direction is to the right as shown in the figure below. Calculate the magnitude and sign of the point charge when the pendulum's position, as shown in a corresponding figure, is 14 cm above its lowest vertical position.
![Diagram showing a charge in equilibrium in an electric field, with measurements and forces indicated.](data:image/png;base64,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)
A small charge with a mass "m" of 2.0 grams is attached to an insulating string that is 60 cm long. This setup is observed to be in equilibrium within a uniform horizontal electric field of 9600 N/C. The electric field direction is to the right as shown in the figure below. Calculate the magnitude and sign of the point charge when the pendulum's position, as shown in a corresponding figure, is 14 cm above its lowest vertical position.