Unit 9: Electromagnetic Induction
A changing magnetic flux, with no battery anywhere, driving a current that always turns out to fight the very change that created it.
9 topics · 32 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.
Magnetic Flux
- How it worksHow does magnetic flux depend on the field's strength, the loop's area, and the angle between them?
- Worked exampleFind the magnetic flux through a 0.1 square meter loop tilted 40 degrees to a uniform 0.6 tesla field.
- Going furtherWhat happens to the flux through a loop as it rotates from lying face-on to lying completely edge-on to the field?
Your turn1 of 2
Find the magnetic flux through a 7 square meter loop tilted 55 degrees to a uniform 8 times 0.1 tesla field.Faraday's Law
- How it worksHow does Faraday's law turn the rate of change of magnetic flux into an induced electromotive force?
- Worked exampleFind the induced emf in a 50-turn, 0.02 square meter coil as its field changes from 0.1 to 0.5 tesla in 0.2 seconds.
- Common mistakeWhy doesn't a steady, unchanging magnetic field passing through a loop induce any current at all?
- Going furtherWhat happens to the induced emf if that same change in flux is made to happen in half the time?
- Worked exampleFind the induced emf in a single loop of area 0.05 square meters if the field through it changes at 2 tesla per second.
Your turn1 of 2
Find the induced emf in a 73 turn, 342 square centimeter coil as its field changes from 5 times 0.1 tesla to 9 times 0.1 tesla in 2 times 0.1 seconds.Lenz's Law
- How it worksHow does an induced current create its own magnetic field that opposes the change in flux that produced it?
- Common mistakeWhy isn't it right to say the induced current opposes the magnetic field itself, rather than the change in flux?
- How it worksWalk me through using Lenz's law to find the induced current's direction as a bar magnet is pushed into a coil.
- Going furtherWhat happens to the direction of the induced current the instant that magnet stops approaching and starts retreating?
Your turn1 of 2
A bar magnet's north pole approaches a wire loop, increasing the flux through it. Which best describes what the induced current in the loop does?Motional EMF
- How it worksHow does the magnetic force on charges inside a moving rod push them to one end and build up an emf?
- Worked exampleFind the motional emf of a 0.4 meter rod sliding at 3 m/s perpendicular to a 0.5 tesla field.
- Common mistakeWhy doesn't a rod sliding parallel to the magnetic field lines generate any motional emf at all?
- Going furtherWhat happens to the motional emf of a sliding rod as its speed along the rails keeps increasing?
- Ties togetherHow does motional emf come out the same whether it's computed from the magnetic force on charges or from Faraday's law?
Your turn1 of 2
Find the motional emf of a 73 cm rod sliding at 13 m/s perpendicular to a 8 times 0.1 tesla field.Induced Electric Fields
- How it worksHow does a time-varying magnetic field curl an electric field around it, the way a steady current curls a magnetic field?
- Common mistakeWhy isn't this induced electric field the same kind of field a static, unmoving charge produces?
- Ties togetherHow does an induced electric field generalize Faraday's law beyond just circuits built out of wire?
Your turn1 of 2
A region of empty space has a magnetic field that is changing over time, but there is no wire or loop present anywhere nearby. Is an electric field created in that region anyway?Eddy Currents
- How it worksHow do swirling eddy currents induced in a moving conductor create a magnetic drag force opposing its motion?
- How it worksWalk me through finding the direction of the eddy currents induced in a metal plate as a magnet approaches it.
- Going furtherWhat happens to the braking effect of eddy currents if the conducting plate has slots cut through it?
Your turn1 of 2
A strong magnet dropped down a vertical copper pipe falls dramatically slower than the same magnet dropped in open air, even though copper is not itself a magnetic material. What causes the slowdown?Electric Generators
- How it worksHow does a rotating loop's changing flux through a field turn mechanical spin into an oscillating emf?
- Worked exampleFind the peak emf of a 200-turn, 0.05 square meter coil spinning at 60 revolutions per second in a 0.3 tesla field.
- Ties togetherHow does a generator run the exact same physics as a motor, just with the mechanical and electrical roles swapped?
Your turn1 of 2
Find the peak emf of a 224 turn, 667 square centimeter coil spinning at 94 revolutions per second in a 3 times 0.1 tesla field.Back EMF in a Motor
- How it worksHow does a spinning motor's own coil generate a back emf that opposes the very current driving it?
- Common mistakeWhy doesn't a motor's back emf mean it's somehow fighting uselessly against its own current?
- Going furtherWhat happens to the current through a motor if something suddenly jams its shaft and stops it from spinning?
Your turn1 of 2
A motor with 14 ohms of coil resistance is connected to a 95 volt supply. Once spinning, it develops a back emf of 37 volts. Find the current through the motor.Applications of Electromagnetic Induction
- How it worksHow does a rapidly alternating magnetic field induce eddy currents directly inside the pan's own metal base?
- How it worksWalk me through how a metal detector senses a buried coin using nothing but induced eddy currents.
- Ties togetherHow does the eddy-current heating in an induction cooktop connect back to the eddy currents that brake a falling magnet?
Your turn1 of 2
An induction cooktop heats a metal pan placed on it, yet the cooktop's own ceramic surface stays cool to the touch. How does this work?