Table of contents
- 0. Math Review31m
- 1. Intro to Physics Units1h 23m
- 2. 1D Motion / Kinematics3h 56m
- Vectors, Scalars, & Displacement13m
- Average Velocity32m
- Intro to Acceleration7m
- Position-Time Graphs & Velocity26m
- Conceptual Problems with Position-Time Graphs22m
- Velocity-Time Graphs & Acceleration5m
- Calculating Displacement from Velocity-Time Graphs15m
- Conceptual Problems with Velocity-Time Graphs10m
- Calculating Change in Velocity from Acceleration-Time Graphs10m
- Graphing Position, Velocity, and Acceleration Graphs11m
- Kinematics Equations37m
- Vertical Motion and Free Fall19m
- Catch/Overtake Problems23m
- 3. Vectors2h 43m
- Review of Vectors vs. Scalars1m
- Introduction to Vectors7m
- Adding Vectors Graphically22m
- Vector Composition & Decomposition11m
- Adding Vectors by Components13m
- Trig Review24m
- Unit Vectors15m
- Introduction to Dot Product (Scalar Product)12m
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- 4. 2D Kinematics1h 42m
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- 6. Intro to Forces (Dynamics)3h 22m
- 7. Friction, Inclines, Systems2h 44m
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- Uniform Circular Motion7m
- Period and Frequency in Uniform Circular Motion20m
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- Opening/Closing Arms on Rotating Stool18m
- Conservation of Angular Momentum46m
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- Heat Transfer44m
- 21. Kinetic Theory of Ideal Gases1h 50m
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- 24. Electric Force & Field; Gauss' Law3h 42m
- 25. Electric Potential1h 51m
- 26. Capacitors & Dielectrics2h 2m
- 27. Resistors & DC Circuits3h 8m
- 28. Magnetic Fields and Forces2h 23m
- 29. Sources of Magnetic Field2h 30m
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- Magnetic Field Produced by Loops and Solenoids42m
- Toroidal Solenoids aka Toroids12m
- Biot-Savart Law (Calculus)18m
- Ampere's Law (Calculus)17m
- 30. Induction and Inductance3h 37m
- 31. Alternating Current2h 37m
- Alternating Voltages and Currents18m
- RMS Current and Voltage9m
- Phasors20m
- Resistors in AC Circuits9m
- Phasors for Resistors7m
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- Inductors in AC Circuits13m
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- Impedance in AC Circuits18m
- Series LRC Circuits11m
- Resonance in Series LRC Circuits10m
- Power in AC Circuits5m
- 32. Electromagnetic Waves2h 14m
- 33. Geometric Optics2h 57m
- 34. Wave Optics1h 15m
- 35. Special Relativity2h 10m
24. Electric Force & Field; Gauss' Law
Gauss' Law
Problem 24i
Textbook Question
Textbook QuestionA 20-cm-radius ball is uniformly charged to 80 nC. (b) How much charge is enclosed by spheres of radii 5, 10, and 20 cm?
Verified step by step guidance
1
Understand that the charge distribution is uniform, meaning the charge density does not change with radius within the ball.
Calculate the total charge density ( ) using the formula , where is the total charge and is the volume of the sphere. The volume of a sphere is given by , where is the radius of the sphere.
For spheres with radii less than or equal to the radius of the charged ball (20 cm), calculate the charge enclosed by using the charge density and the volume of the smaller sphere. Use the formula , where and is the radius of the smaller sphere (5 cm, 10 cm, or 20 cm).
For each radius (5 cm, 10 cm, and 20 cm), plug in the respective values into the volume formula to find and then calculate using the charge density.
Since the charge is uniformly distributed, the charge enclosed by the sphere of radius 20 cm will be equal to the total charge on the ball, which is 80 nC.
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Textbook Question
The nuclei of large atoms, such as uranium, with 92 protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately 7.4×10−15 m. (c) The electrons can be modeled as forming a uniform shell of negative charge. What net electric field do they produce at the location of the nucleus?
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