# Relationship of conductivity and hall voltage to magnetic flux

If an electric current flows through a conductor in a magnetic field, the The presence of this measurable transverse voltage is called the Hall effect after E. H. . We can use a phenomenon called the Hall effect to determine whether the mobile These charges are deflected upward (in the figure) by the magnetic field. The sign of the charge carriers responsible for conduction, the charge .. the magnetic field is 0, control 5 is adjusted to give 0 Hall voltage.

Hall effect for positive charge carriers left and negative charge carriers right. Clearly, it is possible to determine the sign of the mobile charges in a current carrying conductor by measuring the Hall voltage.

If the voltage is positive then the mobile charges are positive assuming that the magnetic field and the current are orientated as shown in the figurewhereas if the voltage is negative then the mobile charges are negative.

If we were to perform this experiment we would discover that the the mobile charges in metals are always negative because they are electrons. However, in some types of semiconductor the mobile charges turn out to be positive. These positive charge carriers are called holes. Holes are actually missing electrons in the atomic lattice of the semiconductor, but they act essentially like positive charges.

Let us investigate the magnitude of the Hall voltage. Suppose that the mobile charges each possess a charge and move along the ribbon with the drift velocity.

The magnetic force on a given mobile charge is of magnitudesince the charge moves essentially at right-angles to the magnetic field. In a steady-state, this force is balanced by the electric force due to the build up of charges on the upper and lower edges of the ribbon. If the Hall voltage isand the width of the ribbon isthen the electric field pointing from the upper to the lower edge of the ribbon is of magnitude.

Now, the electric force on a mobile charge is.

This force acts in opposition to the magnetic force. In a steady-state, giving Note that the Hall voltage is directly proportional to the magnitude of the magnetic field. In fact, this property of the Hall voltage is exploited in instruments, called Hall probes, which are used to measure magnetic field-strength. Suppose that the thickness of the conducting ribbon isand that it contains mobile charge carriers per unit volume. It follows that the total current flowing through the ribbon can be written since all mobile charges contained in a rectangular volume of lengthwidthand thicknessflow past a given point on the ribbon in one second.

A sensor voltage is applied across two terminals and the third provides a voltage proportional to the current being sensed. This has several advantages; no additional resistance a shuntrequired for the most common current sensing method need to be inserted in the primary circuit.

### Hall effect - Wikipedia

Also, the voltage present on the line to be sensed is not transmitted to the sensor, which enhances the safety of measuring equipment. Disadvantages compared with other methods[ edit ] Magnetic flux from the surroundings such as other wires may diminish or enhance the field the Hall probe intends to detect, rendering the results inaccurate. Also, as Hall voltage is often on the order of millivolts, the output from this type of sensor cannot be used to directly drive actuators but instead must be amplified by a transistor -based circuit.

Ways to measure mechanical positions within an electromagnetic system, such as a brushless direct current motor, include 1 the Hall effect, 2 optical position encoder e. When Hall is compared to photo-sensitive methods, it is harder to get absolute position with Hall. Hall detection is also sensitive to stray magnetic fields. Common applications are often found where a robust and contactless switch or potentiometer is required.

Ferrite toroid Hall effect current transducer[ edit ] Diagram of Hall effect current transducer integrated into ferrite ring. Hall sensors can detect stray magnetic fields easily, including that of Earth, so they work well as electronic compasses: To solve this problem, Hall sensors are often integrated with magnetic shielding of some kind.

## Hall effect

For example, a Hall sensor integrated into a ferrite ring as shown can reduce the detection of stray fields by a factor of or better as the external magnetic fields cancel across the ring, giving no residual magnetic flux.

This configuration also provides an improvement in signal-to-noise ratio and drift effects of over 20 times that of a bare Hall device. The range of a given feedthrough sensor may be extended upward and downward by appropriate wiring. To extend the range to lower currents, multiple turns of the current-carrying wire may be made through the opening, each turn adding to the sensor output the same quantity; when the sensor is installed onto a printed circuit board, the turns can be carried out by a staple on the board.

To extend the range to higher currents, a current divider may be used. The divider splits the current across two wires of differing widths and the thinner wire, carrying a smaller proportion of the total current, passes through the sensor. Multiple 'turns' and corresponding transfer function. Split ring clamp-on sensor[ edit ] A variation on the ring sensor uses a split sensor which is clamped onto the line enabling the device to be used in temporary test equipment.

If used in a permanent installation, a split sensor allows the electric current to be tested without dismantling the existing circuit.

### The Hall Effect

Analog multiplication[ edit ] The output is proportional to both the applied magnetic field and the applied sensor voltage. If the magnetic field is applied by a solenoid, the sensor output is proportional to the product of the current through the solenoid and the sensor voltage. As most applications requiring computation are now performed by small digital computersthe remaining useful application is in power sensing, which combines current sensing with voltage sensing in a single Hall effect device.

Power measurement[ edit ] By sensing the current provided to a load and using the device's applied voltage as a sensor voltage it is possible to determine the power dissipated by a device.

Position and motion sensing[ edit ] Hall effect devices used in motion sensing and motion limit switches can offer enhanced reliability in extreme environments. As there are no moving parts involved within the sensor or magnet, typical life expectancy is improved compared to traditional electromechanical switches.

Additionally, the sensor and magnet may be encapsulated in an appropriate protective material. This application is used in brushless DC motors. Hall effect sensors, affixed to mechanical gauges that have magnetized indicator needles, can translate the physical position or orientation of the mechanical indicator needle into an electrical signal that can be used by electronic indicators, controls or communications devices. Its use as an ignition timing device in various distributor types is as follows.

A stationary permanent magnet and semiconductor Hall effect chip are mounted next to each other separated by an air gap, forming the Hall effect sensor.