PES 1120 Spring 2014, Spendier
Lecture 19/Page 1
Today:
- Electric Current (Chapter 26)
- Drift velocity
- Current density
Attention
Up until now, we have been studying electrostatics, in other words no moving charges.
From now on, we are going to allow (in fact, encourage) charges to move.
So, I will have to slightly alter some of the things that I have told you, especially about
conductors.
Current
When you use the term current, most people think of water current flowing down a river.
I will use this analogy frequently, but you are now warned not to take it as a perfect
analogy!
How do we define current?
dV
dx

A  vA
dt Through surface dt
So, if we want to talk about electric current, we have to know something about the
velocity of charges in a material.
Electric Current
Electric current is defined to be the rate at which charge flows through a cross section of
the wire
Now, current, I, is defined as positive in the direction that positive charges move…
Average Current: (Note - I will use capital I not little i as your book does)
q
 Coulomb 
I av 
Unit 
  A ( Ampere)
t
 sec 
∆q is the net charge passing through the cross section
PES 1120 Spring 2014, Spendier
Lecture 19/Page 2
Instantaneous Current:
q dq
I  lim

t  0 t
dt
“Electric current is the amount of charge moving through a surface per time”.
We can find the charge that passes through the plane in a time interval extending from 0
to t by integration:
t
q   dq   Idt
0
Current is not a vector, but we treat it as one. It points in the direction of the electric
field ==> the direction a positive charge would go.
Since the electron was not discovered until 1897 and in 1790 we knew about current, they
did not know at this time that negative charges are moving. Hence we are stuck with this
unfortunate definition of current as a flow of positive charges.
Example 1: During the 4.0 min a 5.0 A current is set up in a wire,
a) how much net charge and
b) how many electrons pass through any cross section across the wire’s width?
These electrons are moving the opposite way to the current flow.
PES 1120 Spring 2014, Spendier
Lecture 19/Page 3
Electric current, just like water current, is conserved:
The current into a junction = current out
Iin = Iout
Example 2: Given I0 = 3A and I1 = 1A, what is I2 and which direction is it flowing?
Iin = Iout
I0 = I1 + I2
I2 = I0 - I1 = (3A)-(1A) = 2A, to the right.
Example 3:
The figure here shows a portion of a circuit. What are the magnitude and direction of the
current I in the lower right-hand wire?
Answer: i = 8A, moving to the right
PES 1120 Spring 2014, Spendier
Lecture 19/Page 4
Average motion of electrons: Drift velocity
- Without an electric field (or no potential difference), charges feel no force, and hence
just move with random motion (because of their thermal energy).
- But, if we apply an electric field (there is a potential difference) in the conductor, there
still is random motion, but on top of that, a net drift in the opposite direction of the field.
Charges are pushed by an electric field inside the conductor. (Since this is NOT an
electrostatic situation. It’s OK to have an electric field inside a conductor.)
- The average motion of the electron against the electric field is called the Drift Velocity

vd . Drift velocities are very small!
PES 1120 Spring 2014, Spendier
Lecture 19/Page 5
I
nAe
So the electric current is related to:
- the drift speed of electrons
- the cross-sectional area of the wire
- the number of conduction electrons on a given volume
vd 
Example 4:
How long does it take electrons to get from a car battery to the starting motor? Assume
the current is 300 A and the electrons travel through a copper wire with cross-sectional
area 0.21 cm2 and length 0.85 m. The number of charge carriers per unit volume is
8.49 x 1028 m-3.
For fun, let's calculate vd:
This is slower than a snail and slug that travel at speeds that vary from 0.013 m/s to
0.0028 m/s.
You may well ask: “If the electrons drift so slowly, why do the room lights turn on so
quickly when I throw the switch?” Confusion on this point results from not
distinguishing between the drift speed of the electrons and the speed at which changes in
the electric field configuration travel along wires. This latter speed is nearly that of light;
electrons everywhere in the wire begin drifting almost at once, including into the light
bulbs. Similarly, when you open the valve on your garden hose with the hose full of
water, a pressure wave travels along the hose at the speed of sound in water. The speed at
which the water itself moves through the hose—measured perhaps with a dye marker—is
much slower.
PES 1120 Spring 2014, Spendier
Lecture 19/Page 6
PHET https://phet.colorado.edu/en/simulation/signal-circuit
Why do the lights turn on in a room as soon as you flip a switch? Flip the switch and
watch the electrons. Does the light turn on immediately? Explain using your observations
of the model.
Current Density
We also find it convenient to define a current density. Current density is defined as the
current per unit cross-sectional area.
J
I
 A
Unit  2 
A
m 
A is the cross-sectional area
One use of current density is in the equation with drift velocity, vd:
vd 
I
J

nAqe nqe
Current Density can be made into a vector:


J  nqe vd
Like current, the direction of current density and drift velocity is OPPOSITE to the
direction of electron motion.
PES 1120 Spring 2014, Spendier
Lecture 19/Page 7
Example 5:
A fuse in an electric circuit is a wire that is designed to melt, and thereby open the circuit,
if the current exceeds a predetermined value. Suppose that the material to be used in a
fuse melts when the current density rises to 440 A/cm2. What diameter of cylindrical wire
should be used to make a fuse that will limit the current to 0.50 A?