Derive the equation of mobility in terms of electric current.
(A) When $n$ electrons move with drift velocity $v_{d}$ in a conductor of cross-sectional area $A$,the electric current $I$ is given by:
$I = n A v_{d} e$
By definition,mobility $\mu$ is the ratio of drift velocity to the applied electric field $E$:
$\mu = \frac{v_{d}}{E}$
Therefore,the drift velocity can be expressed as:
$v_{d} = \mu E$
Substituting this into the current equation:
$I = n A (\mu E) e$
Rearranging the equation to solve for mobility $\mu$:
$\mu = \frac{I}{n A E e}$
The $SI$ unit of mobility is calculated as:
$\mu = \frac{A}{m^{-3} \times m^{2} \times (V/m) \times C} = \frac{A}{V \cdot C} = m^{2} V^{-1} s^{-1}$
$I = n A v_{d} e$
By definition,mobility $\mu$ is the ratio of drift velocity to the applied electric field $E$:
$\mu = \frac{v_{d}}{E}$
Therefore,the drift velocity can be expressed as:
$v_{d} = \mu E$
Substituting this into the current equation:
$I = n A (\mu E) e$
Rearranging the equation to solve for mobility $\mu$:
$\mu = \frac{I}{n A E e}$
The $SI$ unit of mobility is calculated as:
$\mu = \frac{A}{m^{-3} \times m^{2} \times (V/m) \times C} = \frac{A}{V \cdot C} = m^{2} V^{-1} s^{-1}$
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Similar Questions
$(a)$ The electron drift speed is estimated to be only a few $mm\; s^{-1}$ for currents in the range of a few amperes. How then is current established almost the instant a circuit is closed?
$(b)$ The electron drift arises due to the force experienced by electrons in the electric field inside the conductor. But force should cause acceleration. Why then do the electrons acquire a steady average drift speed?
$(c)$ If the electron drift speed is so small,and the electron's charge is small,how can we still obtain large amounts of current in a conductor?
$(d)$ When electrons drift in a metal from lower to higher potential,does it mean that all the 'free' electrons of the metal are moving in the same direction?
$(e)$ Are the paths of electrons straight lines between successive collisions (with the positive ions of the metal) in the $(i)$ absence of electric field,$(ii)$ presence of electric field?
$(b)$ The electron drift arises due to the force experienced by electrons in the electric field inside the conductor. But force should cause acceleration. Why then do the electrons acquire a steady average drift speed?
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$(d)$ When electrons drift in a metal from lower to higher potential,does it mean that all the 'free' electrons of the metal are moving in the same direction?
$(e)$ Are the paths of electrons straight lines between successive collisions (with the positive ions of the metal) in the $(i)$ absence of electric field,$(ii)$ presence of electric field?
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