Hall Effect

Pick an option to see whether it holds. If one of them stops you, the theory page is two steps back.

1. 01

   The Hall effect arises fundamentally due to:

   • a) The resistive heating of the current-carrying conductor
   • b) The Lorentz force acting on moving charge carriers in a magnetic field
   • c) The skin effect at high frequencies
   • d) Thermal diffusion of electrons across the sample
2. 02

   For a rectangular sample carrying current I along the x-axis with magnetic field B applied along the z-axis, the Hall voltage develops along:

   • a) The x-axis (same as current)
   • b) The z-axis (same as field)
   • c) The y-axis, perpendicular to both I and B
   • d) It develops uniformly in all three directions
3. 03

   The Hall coefficient Rₕ = Vₕt / IB. The sign of Rₕ allows you to determine:

   • a) Only the magnitude of carrier concentration
   • b) The mobility of majority carriers
   • c) The type of majority charge carrier (electron or hole)
   • d) The resistivity of the sample
4. 04

   In an n-type semiconductor placed in the standard Hall effect geometry, the Hall field points in a direction such that it:

   • a) Reinforces the Lorentz force on electrons
   • b) Opposes and eventually balances the Lorentz force on electrons at equilibrium
   • c) Acts parallel to the current direction
   • d) Has no relation to the Lorentz force
5. 05

   At equilibrium in the Hall effect, which condition holds for a carrier moving with drift velocity v_d?

   • a) qEₕ = qv_dB, i.e. electric force balances magnetic force
   • b) qEₕ ≫ qv_dB
   • c) qEₕ = 0 always
   • d) v_dB = 0
6. 06

   The carrier concentration n is related to the Hall coefficient by:

   • a) n = 1 / (Rₕq)
   • b) n = Rₕq
   • c) n = Rₕ / q
   • d) n = Rₕq²
7. 07

   Compared to metals, semiconductors are preferred for demonstrating the Hall effect experimentally mainly because:

   • a) Semiconductors have much higher carrier concentration, giving larger Vₕ
   • b) Semiconductors have much lower carrier concentration, giving a measurably larger Hall voltage
   • c) Metals do not exhibit the Hall effect
   • d) Semiconductors are easier to shape into thin samples
8. 08

   If the polarity of the applied magnetic field is reversed while the current direction stays the same, the Hall voltage:

   • a) Remains unchanged in magnitude and sign
   • b) Reverses in sign but keeps the same magnitude
   • c) Becomes zero
   • d) Doubles in magnitude
9. 09

   The Hall mobility μₕ of charge carriers can be calculated using the relation:

   • a) μₕ = Rₕ / σ
   • b) μₕ = Rₕ × σ
   • c) μₕ = Rₕ + σ
   • d) μₕ = σ / Rₕ²
10. 10

    In a real Hall effect measurement, a small "zero-field" voltage often appears across the Hall probes even when B = 0. This is primarily attributed to:

    • a) Carrier concentration being too low to measure accurately
    • b) Misalignment of the Hall probe contacts, causing a small ohmic voltage drop
    • c) The Hall coefficient being negative
    • d) Insufficient current through the sample