AcademyMagnetic Fields and Forces
Academy
Hall Effect
Level 1 - Physics topic page in Magnetic Fields and Forces.
Principle
The Hall effect creates a transverse voltage when moving charges are deflected by a magnetic field.
Notation
\(V_H\)
Hall voltage
\(\mathrm{V}\)
\(I\)
current through the strip
\(\mathrm{A}\)
\(B\)
magnetic field perpendicular to strip
\(\mathrm{T}\)
\(n\)
mobile charge carrier density
\(\mathrm{m^{-3}}\)
\(q\)
carrier charge
\(\mathrm{C}\)
\(t\)
strip thickness along field direction
\(\mathrm{m}\)
Method
Moving carriers are deflected sideways by the magnetic force. Charge separation builds a transverse electric field until electric and magnetic forces balance.
Force balance
\[|q|E_H=|q|v_dB\]
Hall field
\[E_H=v_dB\]
Current density
\[I=n|q|v_dA\]
Hall voltage
\[V_H=\frac{IB}{nqt}\]
The sign of the Hall voltage reveals the sign of the mobile charge carriers.
Rules
Hall field
\[E_H=v_dB\]
Hall voltage
\[V_H=\frac{IB}{nqt}\]
Hall coefficient
\[R_H=\frac{1}{nq}\]
Hall form
\[V_H=\frac{R_HIB}{t}\]
Examples
Question
A metal strip carries
\[2.0\,\mathrm{A}\]
in \[0.50\,\mathrm{T}\]
With \[n=8.0\times10^{28}\,\mathrm{m^{-3}}\]
\[q=1.60\times10^{-19}\,\mathrm{C}\]
and \[t=1.0\,\mathrm{mm}\]
find \(V_H\).Answer
\[V_H=\frac{IB}{nqt}=\frac{(2.0)(0.50)}{(8.0\times10^{28})(1.60\times10^{-19})(1.0\times10^{-3})}=7.8\times10^{-8}\,\mathrm{V}\]
Checks
- The Hall voltage is usually small in metals because carrier density is large.
- Reversing current or magnetic field reverses the Hall voltage sign.
- The thickness in \(V_H=IB/(nqt)\) is the dimension parallel to \(\vec B\).