Hall Effect and Carrier Sign
At equilibrium qE_H + q(v_d cross B) = 0. In the simple one-carrier model, Hall coefficient R_H = 1/(nq), and Hall voltage magnitude is V_H = BI/(n|q|t) for sample thickness t.
Why this shows up in the exam
Identifying carrier sign · Measuring carrier concentration · Magnetic-field sensing
Learn the idea
Magnetic deflection of charge carriers builds a transverse Hall field that reveals carrier sign and density. Carriers moving through a conductor are pushed sideways by the magnetic field. Charge accumulates on opposite faces until the electric Hall force balances the magnetic force.
🧠 Memory hook: Sideways magnetic push builds a Hall voltage until forces balance.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- E_H = v_d B — Hall-field magnitude when drift velocity is perpendicular to B
- R_H = 1/(n q) — single-carrier Hall coefficient including carrier sign
- V_H = B I/(n |q| t) — Hall-voltage magnitude for a rectangular sample
How to approach it
- 1Find carrier velocity and q(v cross B)
- 2Locate charge accumulation and Hall-field direction
- 3Apply force balance or the one-carrier Hall formula
Common slip-ups that cost marks
- •Using conventional-current direction as electron drift direction
- •Ignoring carrier sign when choosing the lower-potential face
- •Using width instead of thickness in the Hall-voltage denominator
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A charge of 2 microC moves perpendicular to a 3 T magnetic field at 4 x 10^5 m/s. Find the magnetic force.
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