The Hall Effect | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

The Hall Effect

A current-carrying slice contains moving charge. A magnetic field pushes those charge carriers sideways.

Charge builds up on opposite edges. This produces a potential difference called the Hall voltage.

Why the Hall voltage appears

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The Hall effect: the field pushes drifting charges sideways. Charge builds up until the electric force balances the magnetic force. The steady Hall voltage is larger when carrier number density n and slice thickness t are smaller.

Moving charge carriers experience a sideways magnetic force.
Charge collects on one edge. The opposite edge is left with the opposite charge.
The separated charges produce an electric field across the slice.
Charge stops building up when the electric force balances the magnetic force.

Derive the Hall-voltage equation

At balance:
$qE=qvB$
$E=\dfrac{V_{\mathrm H}}{d}$
Current depends on carrier number density, cross-sectional area and drift speed.
$I=nAqv \qquad\text{and}\qquad A=dt$
Substitute the drift speed. The width d cancels, leaving the result below.

V_{\mathrm{H}}=\dfrac{BI}{ntq}

Symbols

$V_{\mathrm{H}}$ = Hall voltage (V)
$B$ = magnetic flux density (T)
$I$ = current (A)
$n$ = number density of charge carriers (m⁻³)
$t$ = slice thickness (m)
$q$ = carrier charge magnitude (C)