Induced Electric Fields and Motional EMF · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
به انگلیسی

Motion, flux and induced fields

Science · Electricity & Magnetism · ages 19-21
Name ______________________   Date ____________

  1. For the perpendicular rod-and-rails arrangement, both the magnetic-force calculation and the changing-loop-flux calculation give emf magnitude B l v.

    Circle one:   True   False

  2. A rod of length l moves at speed v perpendicular to uniform B. The rod lies along v cross B. What is its emf magnitude?

    • B l divided by v
    • B l v
    • B v divided by l

  3. Why can electric-field circulation exist around a time-varying magnetic field even when no wire is present?

    • A time-varying magnetic field creates an electric field
    • Air becomes conducting whenever any magnetic flux is present
    • Charges need a wire before any electric field can act on them

  4. In the perpendicular rod-and-rails arrangement, speed doubles while B and rod length stay fixed. What happens to the emf magnitude?

    • It halves
    • It stays the same
    • It doubles

  5. A 2.0 m rod moves at 3.0 m/s perpendicular to a uniform 0.5 T field. The rod lies along v cross B. Give its emf magnitude in volts.

    Answer: ______________

  6. A copper sheet slows as it enters and leaves a magnetic-field region. Where does the mechanical energy removed by eddy-current braking go?

    • Into heat from resistance in the sheet
    • Into new magnetic charge stored in the sheet
    • Into electrons leaving the sheet permanently

  7. A perpendicular rod-and-rails circuit has B = 2 T, l = 1 m and v = 3 m/s. Total resistance is 2 ohms, inductance is negligible and there is no other source. Give the current magnitude in A.

    Answer: ______________

  8. A fixed closed path encloses two regions. With one consistent surface orientation, their flux-change rates are +0.018 Wb/s and -0.006 Wb/s. The electric-field circulation around the matching path direction is -0.024 V.

    Circle one:   True   False

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Motion, flux and induced fields W1-mt_LpmHnz46tu-s1

  1. True · Magnetic force separates charges along the rod, while the increasing loop area changes flux at the same rate B l v.
  2. B l v · This geometry gives a magnetic force along the rod and emf magnitude B l v.
  3. A time-varying magnetic field creates an electric field · Faraday's law relates electric-field circulation to the time derivative of magnetic flux through a fixed path. A wire is not required.
  4. It doubles · The emf magnitude B l v is proportional to v when B, l and orientation are fixed.
  5. 3 · B l v = 0.5 times 2.0 times 3.0 = 3.0 V.
  6. Into heat from resistance in the sheet · Changing flux drives eddy currents. Their magnetic forces oppose motion, and resistance dissipates the removed energy as heat.
  7. 3 · The emf is 2 times 1 times 3 = 6 V. Current is 6 / 2 = 3 A.
  8. False · Add the signed rates: 0.018 + (-0.006) = 0.012 Wb/s. Faraday's law gives circulation -0.012 V, not -0.024 V.
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