Induced Charge and Energy Conservation
With constant circuit resistance and negligible self-inductance, integrating I = emf/R gives the magnitude of total charge as N times flux change divided by R.
Why this shows up in the exam
Ballistic galvanometers · Magnetic-flux measurement · Generator braking calculations
Learn the idea
Total induced charge depends on flux change and resistance, not on how quickly the change occurs. A faster change gives larger emf for less time; a slower change gives smaller emf for more time. When integrated, both transfer the same charge if flux change and resistance are unchanged.
🧠 Memory hook: Emf cares about speed; total charge cares about total flux change.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- q = N |Delta Phi|/R — total induced charge for constant R
- mechanical work = electrical energy + change in stored field energy — energy accounting in induction
How to approach it
- 1Find total flux change
- 2Check that R is constant
- 3Use energy conservation for force or heat
Common slip-ups that cost marks
- •Putting time into q = N Delta Phi/R
- •Using the formula when resistance varies strongly
- •Ignoring magnetic energy stored in an inductor
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A conducting rod of length 2 m moves at 3 m/s perpendicular to a 4 T magnetic field. Find the motional emf.
More from Electromagnetic Induction and Alternating Currents
AC Circuit Analysis and LCR Circuits
AC circuits with resistors, capacitors, and inductors (LCR circuits) exhibit impedance, resonance, phase relationships, and power factor, all crucial for understanding circuit behavior.
AC Generators and Transformers
AC generators convert mechanical energy to electrical energy using electromagnetic induction, while transformers transfer electrical energy between circuits, often changing voltage levels.
Faraday's Law and Lenz's Law
Faraday's law explains how a changing magnetic field induces an electromotive force (EMF), while Lenz's law determines the direction of the induced current to oppose the change causing it.
Self and Mutual Inductance
Self-inductance is the property of a coil to oppose changes in its own current, while mutual inductance is the ability of one coil to induce EMF in another nearby coil.
Eddy Currents and Applications
Eddy currents are circulating currents induced in conductors by changing magnetic fields, leading to energy loss and effects like electromagnetic damping.
Motional EMF
Motional EMF is the voltage induced in a conductor moving through a magnetic field, depending on the speed, length, and orientation of the conductor.