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
49PRACTICE PROBLEM
A metal hoop of radius r has charge +q uniformly spread over it. Find out at what distance from the center along the axis, y = ym, the magnitude of the electric field is maximum.
![Diagram of a charged metal hoop with point P indicating maximum electric field distance.](data:image/png;base64,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)
A metal hoop of radius r has charge +q uniformly spread over it. Find out at what distance from the center along the axis, y = ym, the magnitude of the electric field is maximum.