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
50PRACTICE PROBLEM
In a physics lab, two-point charges are placed along a straight line. Charge Q₁ has a magnitude of -25 μC, while charge Q₂ has a magnitude of 50 μC and is located 15 cm away from charge Q₁. As part of an experiment, you are tasked with finding the distance from Q1 to the point where the electric field is zero.
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)
In a physics lab, two-point charges are placed along a straight line. Charge Q₁ has a magnitude of -25 μC, while charge Q₂ has a magnitude of 50 μC and is located 15 cm away from charge Q₁. As part of an experiment, you are tasked with finding the distance from Q1 to the point where the electric field is zero.