Question

Find the mobility of the conduction electrons in a copper conductor if in Hall effect measurements performed in the magnetic field of induction B=100 mT the transverse electric field strength of the given conductor turned out to be η= 3.1.\[{{10}^{3}}\] times less than that of the longitudinal electric field.

Answer 1

Hint: Mobility is somehow related to the ease with which an electron can move inside the conduction band, and it describes the relationship between the drift velocity of the electrons in the conductor when a potential difference is applied across its ends.

Complete step by step answer:The relationship between drift velocity and an electric field is written as \[{{v}_{d}}=\mu E\]
Here, \[\mu \] is the mobility of the electrons, E is the electric field.
Now as per the question,
$
\mu =\dfrac{{{v}_{d}}}{{{E}_{L}}} \\
\implies {{E}_{T}}={{v}_{d}}B=\dfrac{{{E}_{l}}}{\eta } \\
\therefore \mu =\dfrac{1}{\eta B}=3.2\times {{10}^{-3}}{{m}^{2}}{{V}^{-1}}{{s}^{-1}} \\
$
So, the mobility of electrons comes out to be \[3.2\times {{10}^{-3}}{{m}^{2}}{{V}^{-1}}{{s}^{-1}}\]

Additional Information: If an electric current flows through a conductor in a magnetic field, the magnetic field exerts a transverse force on the moving charges and this force is responsible to push them to one side of the conductor. The buildup of charge at the sides of the conductors will balance this magnetic influence, producing a quantifiable voltage between the two sides of the conductor. This voltage which gets induced due to accumulation of the charges is called the Hall effect. The charge carriers sign determines the direction of the electric field induced.

Note:
Mobility is a tensor quantity. Mobility role comes into play when we talk about the conductivity of semiconductors. The mobility in Semiconductors is a strong function of temperature and impurity concentration.