Unit 1: Electric Charge and the Electric Field
Charge as the source of it all: how two charges push and pull, how that push becomes a field, and how the field survives a whole smear of charge.
9 topics · 37 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 Charge and Conservation of Charge
- Worked exampleFind how many excess electrons sit on a balloon carrying a charge of -8 nanocoulombs.
- How it worksHow does rubbing two materials together strip electrons off one and pile them onto the other?
- Common mistakeWhy doesn't charging an object by friction create any new charge out of nothing?
- Going furtherWhat happens to the total charge on two objects the instant they touch and then separate?
- Worked exampleFind the net charge on two identical 4 nC spheres after they touch, share charge equally, and separate.
Your turn1 of 2
A charged sphere carries a charge of -7 nC. How many excess electrons does it hold? Use e = 1.602x10−19 C.Conductors, Insulators, and Charging by Induction
- How it worksHow do free electrons in a metal rearrange themselves near a charged rod held nearby?
- How it worksWalk me through charging a neutral metal sphere by induction using a rod and a ground wire.
- Common mistakeWhy doesn't the induced charge on a grounded sphere end up with the same sign as the rod?
- Going furtherWhat happens to the separated charge on a sphere the instant its ground wire is disconnected?
Your turn1 of 2
A negatively charged rod is held near, but not touching, a neutral metal sphere. What happens to the sphere's free electrons?Coulomb's Law
- How it worksHow does Coulomb's law turn the distance between two point charges into a 1/r2 force?
- Worked exampleFind the force between a +3 microcoulomb charge and a -6 microcoulomb charge 40 cm apart.
- Worked exampleFind where a third charge must sit on the line between +5 nC and +20 nC to feel zero net force.
- Common mistakeWhy doesn't the more massive of two charged objects get pushed with a smaller force than it exerts?
- Going furtherWhat happens to the Coulomb force between two charges if the distance between them is cut in half?
Your turn1 of 2
Two point charges, +15 nC and -14 nC, sit 47 cm apart. Find the magnitude of the electric force between them. Use k = 8.99x109 N m2/C2.Superposition of Electric Forces
- How it worksHow do the x and y components of three separate forces combine into one net force on a charge?
- Worked exampleFind the net force on a +2 nC charge at one corner of a square with +3 nC at the other three corners.
- Common mistakeWhy doesn't a charge sitting midway between two others automatically feel zero net force?
Your turn1 of 2
A +8 nC charge sits at x = -14 cm and another +8 nC charge sits at x = +14 cm. A +4 nC test charge sits on the y-axis a variable height h (in meters) above the midpoint. Write the magnitude of the net force on the test charge as a function of h. Use k = 8.99x109 N m2/C2.The Electric Field
- How it worksHow does dividing the force on a test charge by its own charge leave behind something the source alone controls?
- Worked exampleFind the electric field 20 cm from a point charge of +5 microcoulombs.
- Ties togetherHow does the electric field turn Coulomb's law into two separate steps: making a field, then feeling a force?
- Going furtherWhat happens to the field a test charge measures as the test charge's own size shrinks toward zero?
- Worked exampleFind the net electric field at the midpoint between a +5 nC and a +5 nC charge held 10 cm apart.
Your turn1 of 2
Find the electric field 34 cm from a point charge of +7 microC. Use k = 8.99x109 N m2/C2.Electric Field Lines
- Common mistakeWhy isn't a field line the actual path a charged particle placed there would go on to travel?
- How it worksHow does the spacing between field lines show you where a field is strong and where it's weak?
- Common mistakeWhy don't two electric field lines ever cross each other in a correctly drawn field diagram?
- Going furtherWhat do the field lines around a dipole look like as you drag the negative charge closer to the positive one?
Your turn1 of 2
In a region containing two point charges, could two different electric field lines ever cross at some point in space?Continuous Charge Distributions by Integration
- How it worksHow does chopping a charged rod into infinitesimal pieces and integrating rebuild its electric field?
- Worked exampleFind the field 15 cm from the center of a uniformly charged 40 cm rod carrying 2 microcoulombs, along its perpendicular bisector.
- Worked exampleFind the electric field on the axis of a charged ring of radius 5 cm and charge 3 nC, 10 cm from its center.
- Going furtherWhat happens to the field on a charged ring's axis once the distance grows much larger than the ring's radius?
Your turn1 of 2
Find the electric field on the axis of a charged ring of radius 8 cm carrying charge 6 nC, at a point 19 cm from its center. Use k = 8.99x109 N m2/C2.The Electric Field of a Charged Disk
- How it worksHow does treating a charged disk as a stack of concentric rings let you integrate your way to its field?
- Worked exampleFind the field on the axis of a charged disk of radius 8 cm and surface density 4 microcoulombs per square meter, 3 cm out.
- Going furtherWhat happens to a disk's field formula as its radius grows so large it looks like an infinite charged plane?
Your turn1 of 2
Find the on-axis electric field of a charged disk of radius 12 cm with surface charge density 6 microC per square meter, at a point 9 cm from its center. Use epsilon0 = 8.85x10−12 C2/(N m2).Electric Dipoles in a Uniform Field
- How it worksHow do equal and opposite charges separated by a small distance combine into a single dipole moment vector?
- Worked exampleFind the torque on a dipole of moment 4 times 10 to the -9 coulomb-meters held at 30 degrees to a 2 times 10 to the 5 N/C field.
- How it worksWalk me through how a uniform field exerts a torque on a dipole but exactly zero net force on it.
- Common mistakeWhy doesn't a dipole sitting in a perfectly uniform electric field ever accelerate off in some direction?
Your turn1 of 2
A dipole of moment 7 times 10−9 C m is held at 55 degrees to a uniform electric field of 8 times 105 N/C. Find the magnitude of the torque on the dipole.