Unit 2: Electric Flux and Gauss's Law
One integral over a closed surface that turns a hopeless sum of point-charge fields into a single number, whenever you're smart about the surface you choose.
8 topics · 31 questions
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Electric Flux Through a Surface
- How it worksHow does the electric flux through a surface depend on the field, the area, and the angle between them?
- Worked exampleFind the electric flux through a 0.5 square meter surface tilted 60 degrees to a uniform 300 N/C field.
- Going furtherWhat happens to the flux through a flat surface as it rotates until it lies exactly edge-on to the field?
Your turn1 of 2
Find the electric flux through a flat surface of area 7 square meters whose normal makes an angle of 75 degrees with a uniform electric field of 619 N/C.Why Gauss's Law Always Holds
- How it worksHow does Gauss's law follow from the very same 1/r2 falloff that shows up in Coulomb's law?
- Common mistakeWhy isn't it true that Gauss's law only works when a charge distribution happens to be symmetric?
- Common mistakeWhy doesn't a charge sitting just outside a closed surface contribute anything to the flux through it?
- Ties togetherHow does Gauss's law let you rederive Coulomb's law for a point charge as one special case of itself?
Your turn1 of 2
Gauss's law relates the total electric flux through any closed surface to the enclosed charge. For which of these charge configurations does Gauss's law hold true?Choosing a Gaussian Surface: Spherical Symmetry
- How it worksHow does spherical symmetry guarantee the field is the same strength everywhere on a sphere centered on the charge?
- Worked exampleFind the electric field 25 cm from a point charge of +6 microcoulombs using a spherical Gaussian surface.
- How it worksWalk me through picking the radius of a Gaussian sphere so it encloses exactly the charge you care about.
- Going furtherWhat happens to this result if the point charge is swapped for any spherically symmetric charge of the same total?
- Worked exampleFind the electric field outside a uniformly charged spherical shell of radius 8 cm and charge 4 microcoulombs, 20 cm from its center.
Your turn1 of 2
Use a spherical Gaussian surface to find the electric field 36 cm from a point charge of +7 microC. Use k = 8.99x109 N m2/C2.The Field Inside a Uniformly Charged Sphere
- Worked exampleFind the field 4 cm from the center of a uniformly charged insulating sphere of radius 10 cm and charge 5 microcoulombs.
- How it worksHow does only the charge inside your Gaussian sphere's own radius end up mattering for the field there?
- Common mistakeWhy doesn't the field inside a uniformly charged sphere grow with distance the same way it does outside?
- Going furtherWhat happens to how the field depends on distance the instant you cross from inside the sphere to outside it?
- How it worksHow does a thin spherical shell of charge produce zero field everywhere inside itself, no matter its thickness?
Your turn1 of 2
Find the electric field 8 cm from the center of a uniformly charged insulating sphere of radius 17 cm and total charge 6 microC, where r is less than a. Use k = 8.99x109 N m2/C2.Choosing a Gaussian Surface: Cylindrical Symmetry
- How it worksHow does choosing a coaxial cylinder around a charged line make the flux integral collapse to one term?
- Worked exampleFind the electric field 15 cm from an infinite line of charge with linear density 4 microcoulombs per meter.
- Going furtherWhat happens to this cylindrical argument once the charged wire has a finite length instead of an infinite one?
- Common mistakeWhy doesn't the field of an infinite charged line fall off as 1/r2 the way a point charge's field does?
Your turn1 of 2
Find the electric field 34 cm from an infinite line of charge with linear density 7 microC per meter. Use k = 8.99x109 N m2/C2.Choosing a Gaussian Surface: Planar Symmetry
- How it worksHow does a pillbox-shaped Gaussian surface straddling a charged sheet make the flux integral trivial?
- Worked exampleFind the electric field near an infinite sheet of charge with surface density 3 microcoulombs per square meter.
- Going furtherWhat happens to the field's strength as you move from very close to an infinite sheet to very far away?
Your turn1 of 2
Find the electric field near an infinite sheet of charge with surface density 7 microC per square meter. Use epsilon0 = 8.85x10−12 C2/(N m2).The Field Between Two Charged Parallel Plates
- How it worksHow do the fields from two oppositely charged sheets add up between the plates and cancel outside them?
- Worked exampleFind the electric field between two oppositely charged plates each with density 2 microcoulombs per square meter.
- Ties togetherHow does this uniform field between two charged plates reappear later as the field inside a parallel-plate capacitor?
Your turn1 of 2
Find the electric field between two oppositely charged parallel plates, each with surface charge density 7 microC per square meter. Use epsilon0 = 8.85x10−12 C2/(N m2).Conductors in Electrostatic Equilibrium
- How it worksHow do free charges inside a conductor rearrange themselves until the interior field vanishes completely?
- How it worksWalk me through why excess charge on any conductor always ends up sitting on its outer surface.
- Common mistakeWhy doesn't charge placed inside a hollow conducting shell simply escape onto the shell's outer surface?
- Going furtherWhat happens to the charge piled up on a conductor's surface wherever that surface has a sharp point?
Your turn1 of 2
The electric field just outside the surface of a charged conductor in equilibrium is 7 times 104 N/C. Find the local surface charge density there. Use epsilon0 = 8.85x10−12 C2/(N m2).