Ch 22: Electric Force & Field; Gauss' LawSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics
Sections
Electric Charge
Charging Objects
Charging By Induction
Conservation of Charge
Coulomb's Law (Electric Force)
Electric Field
Parallel Plate Capacitors
Electric Field Lines
Dipole Moment
Electric Fields in Conductors
Electric Flux
Gauss' Law

Concept #1: Gauss' Law

Practice: Rank the flux through surfaces A, B and C in the figure below from greatest to smallest.

Practice: The flux through the four surfaces of a pyramid are given below 

Φ1 = 10 Nm2 /C     Φ3 = 8 Nm2 /C
Φ2 = 20 Nm2 /C  Φ4 = −15 Nm2 /C 

What is the charge enclosed by the pyramid?

Example #1: Electric Field due to Hollow Shell

Example #2: Surface Charge Density

Practice: A spherical, conducting shell has a charge of –6C. If a 4C charge were placed at the center of the shell, what is the electric field at 4 cm? At 12 cm?

Additional Problems
If more electric field lines leave a gaussian surface than enter it, what can you conclude about the net charge enclosed by that surface? A) is positive B) is negative C) is zero D) depends
A negative charge (-Q) resides at the center of a pyramid with a triangular base. The electric flux through each of the surface is A) -Q/(4ε0) B) Q/(4ε0) C) -Q/ε0 D) Q/ε0 
A solid conducting sphere of radius R1 and total charge q1 is enclosed by a conducting shell with an inner radius R2 and outer radius R3 and total charge q2. OA = a and OC = c.
Some shape is made up of 8 different surfaces. If the electric flux through each surface of the shape is given below, how much charge is enclosed by this shape? Φ1 = 50 Nm2/C                          Φ2 = 75 Nm2/C Φ3 = -150 Nm2/C                       Φ4 = 0 Nm2/C Φ5 = -45 Nm2/C                         Φ6 = 150 Nm2/C Φ7 = 100 Nm2/C                        Φ8 = -125 Nm2/C
A (4.15 m by 4.15 m) square base pyramid with height of 2.53 m is placed in a vertical electric field of 50.1 N/C. Calculate the total electric flux which goes out through the pyramid’s four slanted surfaces.
A spherical surface completely surrounds two charges. Find the electric flux through the surface if the charges are +3.5x10-6 C and -2.3x10-6 C. 
A solid conducting sphere of radius a is placed inside of a conducting shell which has an inner radius b and an outer radius c. There is a charge q1 on the sphere and a charge q2 on the shell.
A cubic box of side a, oriented as shown, contains an unknown charge. The vertically directed electric field has a uniform magnitude E at the top surface and 2 E at the bottom surface.
A point charge 4q > 0 is placed at the center point  O. There is a thick conducting spherical shell with inner radius R2 and outer radius R '2 centered at O. The thickness of this shell is R '2 − R2. Another larger thin concentric spherical shell has radius R3. The thickness of this shell is negligible. The thick shell is charged with a charge 3q and the large thin shell is charged with a charge 9q.
A point charge 4q > 0 is placed at the center point  O. There is a thick conducting spherical shell with inner radius R2 and outer radius R '2 centered at O. The thickness of this shell is R '2 − R2. Another larger thin concentric spherical shell has radius R3. The thickness of this shell is negligible. The thick shell is charged with a charge 3q and the large thin shell is charged with a charge 9q.
The net electric flux through a closed surface is 1. zero if only positive charges are enclosed by the surface. 2. zero if only negative charges are enclosed by the surface. 3. infinite only if the net charge enclosed by the surface if zero. 4. zero if the net charge enclosed by the surface is zero. 5. infinite only if there are no charges enclosed by the surface.
The figure shows four Gaussian surfaces surrounding a distribution of charges. Which Gaussian surfaces have no electric flux through them? (Check all that apply). (a) d (b) a (c) b (d) c
A charge of 10 μC is at the geometric center of a cube. What is the electric flux through one of the faces? The permittivity of a vacuum is 8.85419 × 10−12 C2/N • m2 . 1. 353882.0 2. 171294.0 3. 201411.0 4. 188235.0 5. 116706.0 6. 225882.0 7. 165647.0 8. 263529.0 9. 327529.0 10. 297411.0
A solid conducting sphere of radius R1 and total charge q1 is enclosed by a conducting shell with an inner radius R2 and outer radius R3 and total charge q2. OA = a and OC = c.
A spherical shell has an inner radius of 10 cm and an outer radius of 12 cm. If the spherical shell has a charge Q = 10 nC, and encloses a charge q = -7 nC, what is the surface charge density on the inner surface of the spherical shell?
A point charge Q is placed at the center of a cube of side a. The electric flux through any one of the six sides is a) kQ/a2 b) Q/6ϵ0 c) Q/ϵ0 d) 0 e) can not be determined from the informations provided.
The electric field is constant over each face of the cube shown in the figure. Does the box contain positive charge, negative charge, or no charge?  a) Positive charge b) Negative charge c) No charge
A point charge Q is placed at the center of cube of side a. The electric flux through any one of the six sides is kQ/a2 Q/6εo Q/εo 0 Cannot be determined from the information provided  
A charge is placed in a closed box. If the size of the box doubles, the electric flux going through the boxA) reverse the sign but keeps the same magnitude.B) keeps the same.C) doubles.D) is only half of the original flux.
A point charge q1 is concentric with two spherical conducting thick shells, as shown in the figure below. The smaller spherical conducting shell has a net charge of q2 and the larger spherical conducting shell has a net charge of q3.  What is the charge Q r3 on the inner surface of the larger spherical conducting shell?1. Qr3 = −q1 − q2 + q32. Qr3 = +q13. Qr3 = +q1 − q24. Qr3 = −q15. Qr3 = −q1 − q2 − q36. Qr3 = +q1 + q27. Qr3 = 08. Qr3 = −q1 − q29. Qr3 = +q1 + q2 + q310. Qr3 = −q1 + q2
Gaussian surface A is a cube with side length L and encloses a charge Q. A separate gaussian surface B is a sphere with radius length 10L and encloses a charge Q/2. What is the ratio between the electric fluxes, ΦEA / ΦEB, for these two surfaces? A. 200π/3 B. 3/(200π) C. 2/1 D. 1/1
A conducting spherical shell carrying a charge -5 nC encloses a point charge +5 nC. What is the induced charge (qout) on the "outer" surface of the conducting shell?a. zerob. +5 nCc. -5 nCd. +10 nCe. -10 nC