Unit 3: Electric Potential
Trading vectors for one number that remembers the work it takes to build a charge configuration, and a field you can recover from a potential's slope.
9 topics · 33 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Electric Potential Energy
- How it worksHow does the work done assembling two point charges become the electric potential energy of the pair?
- Worked exampleFind the potential energy of a +4 microcoulomb and a -2 microcoulomb charge separated by 30 cm.
- Common mistakeWhy isn't electric potential energy something a single, isolated charge can be said to have on its own?
- Going furtherWhat happens to the potential energy of two charges as they're pulled apart to an infinite separation?
- Worked exampleFind the total potential energy of three +2 nC point charges placed at the corners of an equilateral triangle of side 10 cm.
Your turn1 of 2
Find the electric potential energy of a +7 microC charge and a -6 microC charge separated by 47 cm. Use k = 8.99x109 N m2/C2.Electric Potential and Voltage
- How it worksHow does moving a charge against a field raise its potential the way lifting a mass raises its potential energy?
- Worked exampleFind the potential difference needed to give a proton 2 times 10 to the -16 joules of kinetic energy from rest.
- Common mistakeWhy doesn't a higher electric potential at a point automatically mean a stronger field is sitting there?
- Ties togetherHow does electric potential play the same role for charge that height plays for mass in gravity?
Your turn1 of 2
Find the potential difference needed to give a proton 7 times 10−16 joules of kinetic energy, starting from rest. Use the proton's charge e = 1.602x10−19 C.The Potential of a Point Charge
- How it worksHow does integrating the electric field along a path from infinity give the potential of a point charge?
- Worked exampleFind the electric potential 50 cm from a point charge of +8 nanocoulombs.
- Going furtherWhat happens to the potential from several point charges as a test charge is moved in from far away?
Your turn1 of 2
Find the electric potential 68 cm from a point charge of +35 nC. Use k = 8.99x109 N m2/C2.Potential of a Continuous Charge Distribution by Integration
- How it worksHow does integrating dq over r turn a whole charged object into a single potential value at one point?
- Worked exampleFind the potential on the axis of a charged ring of radius 6 cm and charge 5 nC, 8 cm from its center.
- Going furtherWhat happens to a charged ring's potential as the observation point moves far beyond the ring's own radius?
Your turn1 of 2
Find the electric potential on the axis of a charged ring of radius 8 cm and charge 6 nC, 19 cm from its center. Use k = 8.99x109 N m2/C2.Equipotential Surfaces
- How it worksHow do equipotential surfaces always end up perpendicular to the field lines that cross through them?
- Common mistakeWhy isn't it possible for two genuinely different equipotential surfaces to touch or cross each other?
- How it worksWalk me through sketching the equipotential surfaces surrounding a single, isolated point charge.
- Going furtherWhat do the equipotential surfaces look like around two equal and opposite point charges?
- Common mistakeWhy doesn't moving a charge along an equipotential surface ever change that charge's kinetic energy?
Your turn1 of 2
Does every point in space sit on exactly one equipotential surface, so that surfaces at two different potential values can never touch or cross?Finding the Electric Field from the Potential
- How it worksHow does taking the negative slope of the potential in a direction give the field component in that direction?
- Worked exampleFind the electric field between two plates 2 cm apart held at a potential difference of 500 volts.
- Common mistakeWhy doesn't a region of high potential have to be a region where the electric field is especially strong?
- Going furtherWhat happens to the electric field wherever the potential is flat, with no change from point to point?
Your turn1 of 2
Find the electric field between two plates 7 cm apart held at a potential difference of 667 volts.Why a Whole Conductor Sits at One Potential
- How it worksHow does the zero field inside a conductor force its entire volume to share a single potential value?
- Common mistakeWhy doesn't a conductor's irregular shape create different potentials at different points on its own surface?
- Ties togetherHow does a conductor being one equipotential connect back to the field vanishing throughout its interior?
Your turn1 of 2
A charged conducting sphere of radius 15 cm carries charge 13 nC. Find the electric potential at its surface, which also equals the potential everywhere inside it. Use k = 8.99x109 N m2/C2.Energy in Electron Volts
- How it worksHow does accelerating a charge through a one-volt potential difference define the electron volt as a unit?
- Worked exampleFind the kinetic energy in electron volts of an electron accelerated through a potential difference of 4000 volts.
- Going furtherWhat happens to the size of the natural energy unit when you're describing a proton instead of an electron?
Your turn1 of 2
Find the kinetic energy, in electron volts, of an electron accelerated through a potential difference of 6995 volts.Applications of Electrostatics
- How it worksHow does a moving belt keep piling charge onto a hollow metal sphere until sparks fly off its surface?
- How it worksWalk me through how a lightning rod protects a building by controlling where the field grows strongest.
- Ties togetherHow does charge piling up at sharp points explain both a lightning rod and a Van de Graaff generator?
Your turn1 of 2
A Van de Graaff generator uses a moving belt to carry charge onto a large hollow metal dome. Where does essentially all of that charge end up once it reaches the dome?