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Boss lesson · The Induction Gauntlet
Exam-hall rules, last bench
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Exam-hall rules, last bench

This is the boss. No calculator — today μ0=1.25×10−6 T⋅m/A\mu_0 = 1.25\times 10^{-6}\ \mathrm{T\cdot m/A}, the round number kept for mental work and bench sanity checks, and every value on the page is chosen to fit in your head. One rig, one long problem, and every answer feeds the next: the solenoid's field, then the flux it drives through the search coil, then the EMF as that flux collapses, then the EMF the sliding bar makes in the same field. Write each line down as you go — one early slip rolls all the way to the last.

Watch what the final line actually asks. It does not want another number; it wants a DECISION between two ways of generating, the way a real bench comparison does. The arithmetic is only there to earn you the right to make it.

Everything in the chapter rides in this one bench. 5★ under par here is the chapter crown. Clock in.

INBL

B=μ0NILB = \frac{\mu_0 N I}{L}

  • BB= Magnetic field (magnetic flux density)
  • NN= Number of turns
  • II= Current (electric current)
  • LL= Solenoid length (length)
Magnetic Field of a Solenoid solver →
θBΦA

Φ=BAcos⁡θ\Phi = B A \cos\theta

  • Φ\Phi= Magnetic flux (magnetic flux)
  • BB= Magnetic field (magnetic flux density)
  • AA= Loop area (area)
  • θ\theta= Tilt angle (angle)
Magnetic Flux (Φ = BA cos θ) solver →
εΔΦΔtN

ε=NΔΦΔt\varepsilon = N \frac{\Delta\Phi}{\Delta t}

  • ε\varepsilon= Induced EMF (voltage)
  • NN= Number of turns
  • ΔΦ\Delta\Phi= Flux change (magnetic flux)
  • Δt\Delta t= Time interval (time)
Faraday's Law of Induction solver →
vεBL

ε=BLv\varepsilon = B L v

  • ε\varepsilon= Motional EMF (voltage)
  • BB= Magnetic field (magnetic flux density)
  • LL= Conductor length (length)
  • vv= Speed (speed)
Motional EMF (ε = BLv) solver →
no calculator in the boss room — the numbers are chosen to fit in your head