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 Field
24. Electric Force & Field; Gauss' Law
Electric Field: Study with Video Lessons, Practice Problems & Examples
51PRACTICE PROBLEM
Two unknown charges, Q₁ and Q₂, are placed far apart. At a point halfway between charges Q₁ and Q₂, the electric field is zero. What is the ratio of charge Q₁ to charge Q₂?
![Diagram showing two charges Q1 and Q2 with electric field E=0 at midpoint, illustrating charge ratio question.](data:image/png;base64,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)
Two unknown charges, Q₁ and Q₂, are placed far apart. At a point halfway between charges Q₁ and Q₂, the electric field is zero. What is the ratio of charge Q₁ to charge Q₂?