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 Lines
24. Electric Force & Field; Gauss' Law
Electric Field Lines: Study with Video Lessons, Practice Problems & Examples
5PRACTICE PROBLEM
Imagine a spherical shell where the inner surface has a negative charge while the outer surface has an equivalent positive charge as shown in the figure. Draw this figure on your paper, then sketch out the direction of electrical fields.
![Spherical shell with inner negative and outer positive charges, showing electric field directions.](data:image/png;base64,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)
Imagine a spherical shell where the inner surface has a negative charge while the outer surface has an equivalent positive charge as shown in the figure. Draw this figure on your paper, then sketch out the direction of electrical fields.