Question
Define mobility and write its formula, unit and dimensional formula.
✓
Answer
→ Conductivity of conductor arises from mobile charge carriers.
→ In metals, electrons are mobile charge carriers. In an electrolyte they are positive and negative ions while in an ionised gas, they are electrons and positive charged ions. In semi conductors, free electrons and holes are mobile charge carriers.
→ "The magnitude of the drift velocity per unit electric field is called the mobility ( $\infty$ )."
$
\infty=\frac{\left|\overrightarrow{v_d}\right|}{E} \ldots
$
→ The SI unit of mobility is $m^2 / Vs$ and practical unit is $cm ^2 / Vs$
→ Dimensional formula of mobility is $M ^{-1} L^0 T^2 A^1$
→ Using drift velocity $\left|\vec{v}_d\right|=\frac{ Ee }{m} \cdot \tau$
in equation (1).
we get,
$
\begin{array}{l}
\propto=\frac{\frac{e E}{m} \tau}{E} \\
\therefore \propto=\frac{e \tau}{m}
\end{array}
$
where $\tau$ is the average collision time for electrons.
→ In metals, electrons are mobile charge carriers. In an electrolyte they are positive and negative ions while in an ionised gas, they are electrons and positive charged ions. In semi conductors, free electrons and holes are mobile charge carriers.
→ "The magnitude of the drift velocity per unit electric field is called the mobility ( $\infty$ )."
$
\infty=\frac{\left|\overrightarrow{v_d}\right|}{E} \ldots
$
→ The SI unit of mobility is $m^2 / Vs$ and practical unit is $cm ^2 / Vs$
→ Dimensional formula of mobility is $M ^{-1} L^0 T^2 A^1$
→ Using drift velocity $\left|\vec{v}_d\right|=\frac{ Ee }{m} \cdot \tau$
in equation (1).
we get,
$
\begin{array}{l}
\propto=\frac{\frac{e E}{m} \tau}{E} \\
\therefore \propto=\frac{e \tau}{m}
\end{array}
$
where $\tau$ is the average collision time for electrons.
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