Falling Plate in a Magnetic Field

A metal plate released from rest in a uniform field out of the page — what really happens?

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Parameters

1.0 T
0.40 m

Live Data

Time t 0.00 s Velocity v = gt 0.00 m/s Acceleration a 9.81 m/s² EMF ε = Bvw 0.00 V Induced current I 0 (no circuit!)

v–t Graph

Straight line with slope g — free fall is unaffected.

Legend

  • Velocity (v)
  • Acceleration (a = g)
  • Magnetic force on electron (F)
  • Magnetic field B (out of page ⊙)

Exam Question (HKDSE style)

A rectangular metal plate parallel to the vertical is released from rest inside a uniform magnetic field pointing out of the page. Neglect air resistance. Which of the following statements is correct?

Physics Explained

  • As the plate falls with velocity v, each free electron inside it moves through the field B. The magnetic force F = Qv×B pushes electrons towards side XY, leaving side WZ positively charged.
  • Charge separation stops growing when the internal electric force balances the magnetic force (eE = evB). A voltage ε = Bvw therefore appears across WZ and XY — statement B is correct.
  • There is no closed circuit, and the field is uniform, so the magnetic flux through any loop inside the plate never changes. No current flows — statement A is wrong.
  • With no current, there is no magnetic braking force. The only force is gravity, so the plate falls with acceleration g — statements C and D are wrong.