Hall Effect

If an electric current flows through a conductor in a magnetic field, the magnetic field exerts a transverse force on the moving charge carriers which tends to push them to one side of the conductor. This is most evident in a thin flat conductor as illustrated. A buildup of charge at the sides of the conductors will balance this magnetic influence, producing a measurable voltage between the two sides of the conductor. The presence of this measurable transverse voltage is called the Hall effect after E. H. Hall who discovered it in 1879.

Note that the direction of the current I in the diagram is that of conventional current, so that the motion of electrons is in the opposite direction. That further confuses all the "right-hand rule" manipulations you have to go through to get the direction of the forces.

The Hall voltage is given by Hall电压由 VH = IB/ned V H = IB/ned（专名或术语） Show 显示 where n = density of mobile charges and e = electron charge. The Hall effect can be used to measure magnetic fields with a Hall probe. 霍尔效应可以用来测量磁场，使用霍尔探头。 其中，n 为自由电荷的密度，e 为电子电荷。

Hall Voltage for Positive Charge Carriers

The transverse voltage (Hall effect) measured in a Hall probe has its origin in the magnetic force on a moving charge carrier.

The magnetic force is F_m = ev_dB where v_d is the drift velocity of the charge.

The current expressed in terms of the drift velocity is 以漂移速度表示的电流是 I = neAvd I = neAv d（专名或术语） Show 显示 where n is the density of charge carriers. Then 其中n是载流子的密度。然后 Fm = eIB/neA F_m = eIB/neA

At equilibrium

And substituting gives

Hall Probe

The measurement of large magnetic fields on the order of a Tesla is often done by making use of the Hall effect. A thin film Hall probe is placed in the magnetic field and the transverse voltage (on the order of microvolts) is measured.

Sometimes a thin copper film of thickness d on the order of 100 micrometers is used for a Hall probe. Taking the charge carrier density to be 有时会使用厚度约为100微米的薄铜膜作为霍尔探头。将载流子密度取为 n=8.47x1028 electrons/m3 n=8.47×10²⁸ 电子/立方米 Show 显示 For I = amperes magnetic field B = Tesla and d = x10^ meters. The Hall voltage is VH = IB/ned = x10^ volts. x10^伏特。 中文译文中的待填/计算数值依次对应：1：vb 2：vp。实际数值以上方原输入框为准。 对于 I = 安培，磁场 B = 特斯拉，d = 10^x 米。霍尔电压是 V_H = IB/(ned)。 中文译文中的待填/计算数值依次对应：1：i 2：b 3：db 4：dp。实际数值以上方原输入框为准。

Charge Carriers in the Hall Effect

The Hall effect is a conduction phenomenon which is different for different charge carriers. In most common electrical applications, the conventional current is used partly because it makes no difference whether you consider positive or negative charge to be moving. But the Hall voltage has a different polarity for positive and negative charge carriers, and it has been used to study the details of conduction in semiconductors and other materials which show a combination of negative and positive charge carriers.

The Hall effect can be used to measure the average drift velocity of the charge carriers by mechanically moving the Hall probe at different speeds until the Hall voltage disappears, showing that the charge carriers are now not moving with respect to the magnetic field. Other types of investigations of carrier behavior are studied in the quantum Hall effect.