Moving Loops and Changing Overlap Area
For perpendicular uniform B, Phi = B times overlap area. The emf is B times the rate at which that overlap area changes.
Why this shows up in the exam
Magnetic speed sensors · Electromagnetic braking · Loop-entry graph problems
Learn the idea
A loop entering or leaving a field has emf because its area inside the field changes. Only the portion of the loop inside the magnetic region contributes to flux. During entry or exit, that overlap changes; when the whole loop moves inside a uniform field, flux is constant.
🧠 Memory hook: Entry changes area; fully inside changes position, not flux.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- emf = B dA_overlap/dt — magnitude for perpendicular uniform field
- F_external v = I² R — mechanical power becomes electrical heating at steady speed
How to approach it
- 1Sketch overlap area versus position
- 2Differentiate or find its slope
- 3Use Lenz's law for sign or direction
Common slip-ups that cost marks
- •Assuming motion always means induction
- •Using total loop area during partial entry
- •Missing different entry and exit intervals
🌟 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.
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