QiLing Tools

🧲Hall Effect & Crossed-Field Devices - Hall voltage, mass spectrometer, cyclotron

Starting from the Hall effect, this tool gathers the devices where an electric and a magnetic force balance. In a Hall slab, electrons or holes are pushed to one face until the Hall field cancels the magnetic force; the animation shows this, and the tool gives the Hall voltage, drift speed and which face is higher for copper, n- and p-type silicon, InSb and GaAs (approximate densities). You can work backwards from a measured voltage to the carrier density and type, and read short notes on clamp meters, Hall speed sensors and brushless motors. The velocity selector, MHD generator, electromagnetic flowmeter, mass spectrometer and cyclotron each have adjustable animations, derivations and results, followed by random practice problems.

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How to use Hall Effect & Crossed-Field Devices

  1. 1On Hall effect, choose a material and set the current, field, thickness and width; watch the carriers and the Hall voltage
  2. 2On Find carriers, enter a measured voltage with its sign to get the carrier density and type
  3. 3Open the velocity selector, MHD generator, flowmeter, mass spectrometer and cyclotron tabs and adjust their parameters
  4. 4Use the Practice tab for random problems marked instantly

FAQ

Where does U_H = IB/(nqd) come from?
Carriers drifting at v feel qvB and pile up on one face, creating a field E_H. In equilibrium qE_H = qvB, and E_H = U_H/b, so U_H = Bvb. With I = nqv·bd, v = I/(nqbd), giving U_H = IB/(nqd), where d is the thickness along B; the width b cancels.
How does the Hall effect tell n-type from p-type?
Electrons and holes move in opposite directions but carry opposite charges, so both are pushed to the same face. If holes collect there that face is at the higher potential; if electrons collect, it is lower. Knowing the current and field directions, the sign of the Hall voltage gives the carrier type, and n = IB/(|U|ed) gives the density.
Why are Hall sensors made of semiconductors?
U_H is inversely proportional to the carrier density. Copper has about 8.5×10²⁸ electrons per m³, so its Hall voltage is only nanovolts; doped semiconductors have 10²¹ to 10²² m⁻³ and give millivolts to volts, so they are far more sensitive.
What do the velocity selector, MHD generator and flowmeter have in common?
In each, the electric force balances the magnetic force: qE = qvB. A velocity selector passes only v = E/B, whatever the charge, sign or mass, provided the particle enters from the correct side. In an MHD generator or flowmeter, moving charges collect on the plates or pipe walls until qU/d = qvB, so U = Bdv; for the flowmeter Q = πd²v/4 = πdU/(4B).
Does a cyclotron's maximum energy depend on the gap voltage?
No. The particle leaves when its radius reaches the dee radius R, and R = mv/(qB) gives Ek = q²B²R²/(2m), set only by B and R. A higher gap voltage means fewer accelerations, n = Ek/(qU), and a shorter total time t = πBR²/(2U). The voltage frequency must match the cyclotron frequency f = qB/(2πm).

Features

  • Animated carrier deflection and charge build-up for electrons or holes, with switchable field direction
  • U_H = IB/(nqd), drift speed, Hall field, Hall coefficient and sensitivity, plus inverse carrier density and type
  • Hall sensor applications: clamp-meter output, speed from pulse rate and brushless motor commutation
  • Velocity selector with true numerical trajectories, several particles and reversed entry
  • MHD generator, flowmeter, mass spectrometer with isotope landing points, and a cyclotron spiral with maximum energy
  • Eight kinds of random problems: Hall voltage, carrier density, selected speed, EMF, flow, landing distance, energy and time