Magnetic Braking of a Falling Magnet
A strong neodymium magnet is dropped through a vertical copper tube of length 1.2 m. The magnet reaches a terminal velocity well before the bottom, taking 3.5 s to fall the full length, compared with 0.49 s in free fall. A student claims the magnet is being repelled by the copper, which they believe is magnetic. A second student claims the copper is magnetised by induction and attracts the magnet. A third suggests eddy currents are responsible. The tube is then replaced with a plastic tube of identical dimensions and the fall time returns to 0.49 s.
1. Evaluate each student's claim using Faraday's and Lenz's laws, and explain why the plastic tube gives free-fall timing.
Read the worked answer
Claim 1 (repulsion because copper is magnetic): Incorrect. Copper is not ferromagnetic; it does not attract a magnet at rest. A stationary magnet in a copper tube experiences no force.
Claim 2 (attraction from induced magnetisation): Partially right but misstated. The changing flux as the magnet moves induces eddy currents in the copper. By Lenz's law these currents create a field that opposes the change in flux - above the magnet the induced pole repels, below it attracts - but the net effect is a drag force opposing motion, not a static attraction.
Claim 3 (eddy currents): Correct. The moving magnet changes the flux through loops of copper, inducing currents that dissipate energy as heat and exert a retarding force proportional to velocity.
Plastic tube: Plastic is an insulator; eddy currents are negligible, so no magnetic drag. Fall time matches free fall.
2. Estimate the average retarding force on the magnet if its mass is 20 g, and explain why the magnet reaches terminal velocity.
Read the worked answer
Free fall: t = √(2h/g) = √(2 × 1.2/9.8) = 0.495 s, matching the quoted 0.49 s.
Net acceleration in copper: Using s = ½at², a = 2 × 1.2/(3.5²) = 0.196 m/s².
Net force: F_net = ma = 0.020 × 0.196 = 3.9 × 10⁻³ N downward.
Retarding force: F_drag = mg − F_net = 0.020 × 9.8 − 3.9 × 10⁻³ = 0.196 − 0.0039 ≈ 0.192 N.
Terminal velocity: The drag force grows with speed (F ∝ v because induced emf ∝ v and current ∝ emf). When F_drag = mg, net force is zero and the magnet falls at constant speed. The 3.5 s fall time reflects mostly this terminal-velocity phase, not uniform acceleration - so the 'average acceleration' above is a rough estimate only.