Transcript Unit 3, Day 4: Microscopic View of Electric Current

Unit 3, Day 4: Microscopic View of
Electric Current
• Current Density
• Drift Velocity
• Speed of an Electron in as Wire
• Electric Field inside a Current Carrying
Conductor
Current Density
• When a potential difference is applied across a
conducting wire, an electric field is generated parallel to
the walls of the wire
• Inside the conductor, the E-field is no longer zero,
because charges are free to move within the conductor
• Current Density is defined as the current through the
wire per unit of Cross-Sectional Area
I
j  or I  j  A
A
• If the current density is not uniform:
I   jdA
• The direction of j is usually in the direction of the E-Field
Drift Velocity
• When the E-Field is first applied, the electrons
initially accelerate but soon reach a more or less
steady state average velocity.
• This average velocity is in the direction opposite
of the E-Field and is known drift velocity
• Drift velocity is due to electrons colliding with
metal atoms in the conductor
Drift Velocity Calculation
• n - Free electrons (of charge e) travel a displacement l,
in a time Δt, through a cross-sectional area A, at a
current density j, The drift velocity is:
j
I
vD  
or 
ne
neA
• Note: the (-) sign indicates the direction of (positive conventional) current, which is opposite to the direction
of the velocity of the electrons
Speed of an Electron in a Wire
• Given: Cu wire, Φ=3.2 mm (r = 1.6 x 10-3m)
I=5.0A, T = 20°C (293 K), assuming 1 free electron per
atom:
N # e  ( in 1 mole)
28 e 
n 
 8.4  10 m 3
m (1 mole)
V
e
I
I
5 m
vD 


4
.
6

10
s
2
neA ne  r
• Note: the rms velocity of thermal electrons in an ideal
gas is a factor of 109 faster! 1.2  105 ms


Electric Field inside a Current
Carrying Conductor
• Current carrying conductor of length l and crosssectional area A, having resistance R, with a
potential difference across it of ΔV
l
Re member R   , I  j  A, & V  E  l
A
If V  I  R
l
Then E  l  j  A    jl
A
or E  j
Writing it another way j 
E

 E