Question

Hall effect is used to measure ?

Answer 1

Hint: We need to know about the concept of Hall effect and its applications.Hall effect is a phenomenon that relates the applied magnetic field with the current density and the related parameters. It is due to the production of a transverse electric field.

Complete step by step answer:
Hall effect was discovered in 1879 by Edwin Herbert Hall. When a perpendicular magnetic field is applied to a current carrying conductor, a measurable amount of voltage is produced. This is known as the Hall effect. The voltage is known as Hall voltage.Hall effect is used to measure the carrier concentration of the materials to categorize them as semiconductors or insulators.

Equilibrium is reached within the conductor when the magnetic force equals the electric force.
$eE = e{v_d}B$
where $e$ is the electronic charge, $E$ is the electric field, $B$ is the magnetic field and ${v_d}$ is the drift velocity.
$ \Rightarrow {v_d} = \dfrac{E}{B}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,........(1)$
Now current flowing through a conductor can be given as $I = neA{v_d}$ where I is the current flowing through the conductor, n is the number of charge carriers per volume, A is the cross sectional area of the conductor.
Substituting from equation (1) we get,
$I = neA(\dfrac{E}{B})\,\,\,\,\,\,\,\,\,\,\,\,\,\,.......(2)$

Now the potential gradient would give us the electric field.
Hence, $E = \dfrac{V}{l}$ where V is the Hall voltage and l is the length of the conductor.
Substituting in the equation and then rearranging we get,
$V = \dfrac{{IBl}}{{neA}}\,\,\,\,\,\,\,\,\,\,\,\,.........(3)$
The current flowing in the circuit can be measured with an ammeter, Hall voltage by voltmeter. For a given conductor material, $\dfrac{l}{A}$ is specified. The applied magnetic field is also known.Thus, by substituting the values in the above formula, we calculate the carrier concentration in a material.

Hence, hall effect is used to measure carrier concentration in a material.

Note: The Hall voltage can be used to determine which type of charge carriers are present inside a material. If the sign of Hall voltage is negative, then electrons are the majority charge carriers and if the sign is positive, holes are the majority charge carriers. In most metals, electrons are the charge carriers except tungsten and beryllium.