PX157 - B13a - current

current

amount of charge flowing though a specific area per unit time:

I = \frac{d Q}{d t}

units: $C s^{- 1}$ or $a m p e r e (A)$

current density vector

current per unit cross sectional area:

\vec{J} = \frac{I}{A} \hat{z} = n q {\vec{v}}_{d}

where, $n =$ number density, $q =$ charge, ${\vec{v}}_{d} =$ mean velocity of charges / drift velocity

units: $A m^{- 2}$
points in the same direction as $\vec{E}$

drift velocity

in time, $Δ t$ , free charges will move a distance, $v_{d} Δ t$
volume of the region passing $P :$

V o l . = v_{d} Δ t A

number of charges passing point $P :$

N = n V o l . = n v_{d} Δ t A

charge passing $P$ in $Δ t :$

Δ Q = | q | n v_{d} Δ t A

current:

I = \frac{Δ Q}{Δ t} = | q | n v_{d} A

eg: for copper
$A = π (1.02 m m)^{2}$
$n = 8.47 \times 10^{28} m^{- 3}$
$I = 1.67 A$ $∴ v_{d} \approx 1.5 \times 10^{- 4} m s^{- 1}$
- also, random motion in material, $v_{r a n d o m} = 10^{6} m s^{- 1}$