Potential at a Certain Location. q 2. r 2. q 1. A. r 1. 2. Travel along a path from point very far away to the location of interest and add up at each step:. q 2. q 1. dl. A. E. 1. Add up the contribution of all point charges at this point. Common Pitfall.
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q2
r2
q1
A
r1
2. Travel along a path from point very far away to the location of interest and add up at each step:
q2
q1
dl
A
E
1. Add up the contribution of all point charges at this point
Assume that the potential V at a location is defined by the electric field at this location.
A
Example: E = 0 inside a charged metal sphere, but V is not!
A negative test charge Q = 0.6C was moved from point A to point B In a uniform electric field E=5N/C. The test charge is atrestbefore and after the move. The distance between A and B is 0.5m and the line connecting A and B is perpendicular to the electric field. How much work was done by the net external force while moving the test charge from A to B?
A
E = 5 N/C
0.5m
B
After moving the 0.6C test charge from A to B, it was then moved from B to C along the electric field line. The test charge is at restbefore and after the move. The distance between B and C also is 0.5m. How much work was done by the net external force while moving the test charge from A to C?
E = 5 N/C
0.5m
C
B
A
Instead of moving the test charge from A to B then to C, it is moved from A to D and then back to C. The test charge is at restbefore and after the move. How much work was done by the net external force while moving the test charge this time?
A
D
E = 5 N/C
0.5m
0.5m
B
C
+1.5 J of work was done by the net external force while moving the 0.6 C test charge from B to C. The test charge is at restbefore and after the move. What is the voltage difference between B and C, and at which point is the voltage larger?
A
D
E = 5 N/C
0.5m
0.5m
B
C
Magnetic Field
A compass needle turns and points in a particular direction
there is something which interacts with it
Magnetic field (B): whatever it is that is detected by a compass
Compass: similar to electric dipole
Magnetic fields are produced by moving charges
Current in a wire: convenient source of magnetic field
Static equilibrium: net motion of electrons is zero
Can make electric circuit with continuous motion of electrons
The electron current (i) is the number of electrons per second that enter a section of a conductor.
Counting electrons: complicated
Indirect methods:
measure magnetic field
measure heating effect
Both are proportional to the electron current
We use a magnetic compass as a detector of B.
How can we be sure that it does not simply respond to electric fields?
Compass needle:
Interacts with iron, steel – even if they are neutral
Unaffected by aluminum, plastic etc., though charged objects polarize and interact with these materials
Points toward North pole – electric dipole does not do that
Imagine anelectric circuit:
What is the effect on the compass needle?
What if we switch polarity?
What if we run wire under compass?
What if we change the current or there is no current in the wire?
Hans Christian Ørsted
(1777  1851)
Experimental results:
Oersted effect:
discovered in 1820 by H. Ch. Ørsted
How does the field around a wire look?
Principle of superposition:
The moving electrons in a wire create a magnetic field
What can you say about the magnitudes of BEarthand Bwire?
What if BEarth were much larger than Bwire?
A currentcarrying wire is oriented NS and laid on top of a compass. The compass needle points 27o west. What is the magnitude and direction of the magnetic field created by the wire Bwire if the magnetic field of Earth is BEarth= 2105 T (tesla).
JeanBaptiste Biot
(17741862)
Felix Savart
(17911841)
Nikola Tesla
(18561943)
Electric field of a point charge:
Moving charge makes a curly magnetic field:
B units: T (tesla) = kg s2A1
High tension coil demonstration
Calculate magnitude:
Calculate direction:
Righthand rule
A
) +x
W
h
a
t i
s
t
he
d
ir
e
ct
i
o
n
o
f
B
) –
x
C
) +y
D
) –
y
<
0
,
0
,
3
> x < 0
,
4
,
0
>
?
E
)
z
er
o m
ag
n
it
u
d
e
B
B
B
B
B
a vector (arrow) is facing out of the screen
r
v
Why must the field change direction above and below the dashed line?
What is B straight ahead?
What if the charge is negative?
B1
B2
B3
r
v
Which is larger, B1or B3?
Which is larger, B1or B2?
r
v
B1
B1
r
v
r
v
B
+
Magnetic field depends on qv:Positive and negative charges produce the same B if moving in opposite directions at the same speed

For the purpose of predicting B we can describe current flow in terms of ‘conventional current’ – positive moving charges.

An electron passing through the origin is traveling at a constant velocity in the negative y direction. What is the direction of the magnetic field at a point on the positive z axis?
y
x
+x
z
+z
No magnetic field
x
v
z
A currentcarrying wire lies on top of a compass. What is the direction of the electron current in this wire?
What would the direction of conventional current have to be?
Any magnetic field?
charged tape
Electric fields: produced by charges
Magnetic fields: produced by moving charges
Must use the velocities of the charges as you observe them in
your reference frame!
There is a deep connection between electric field and magnetic fields (Einstein’s special theory of relativity)
If we suddenly change the current in a wire:
Magnetic field will not change instantaneously.
Electron and positron collide: Produce both electric and magnetic field, these fields exist even after annihilation.
Changes propagate at speed of light
There is no time in BiotSavart law:
Speed of moving charges must be small
A steady flow of charges in one direction will create a magnetic field. How can we cause charges to flow steadily?
Need to find a way to produce and sustain E in a wire.
Use battery
mobile
electron
density
wire
Cross sectional
area
Average
drift
speed
Electron current:
Typical electron current in a circuit is ~ 1018 electrons/s.
What is the drift speed of an electron in a 1 mm thick copper wire of circular cross section?
How much time would it take for a particular electron to move
through a piece of wire 30 cm long?
How can a lamp light up as soon as you turn it on?
In some materials current moving charges are positive:
Ionic solution
“Holes” in some materials (same charge as electron but +)
Observing magnetic field around copper wire:
Can we tell whether the current consists of electrons or positive ‘holes’?
The prediction of the BiotSavart law is exactly the same in either case.
André Marie Ampère
(1775  1836)
Metals: current consists of electrons
Semiconductors:
ntype – electrons
ptype – positive holes
Most effects are insensitive to the sign of mobile charges:
introduceconventional current:
Units: C/s A (Ampere)
A typical electron current in a circuit is 1018 electrons/s.
What is the conventional current?
Superposition principle is valid
The BiotSavart law for a short length of thin wire
Single Charge:
The BiotSavart law for a short length of thin wire
Current:
Moving charge produces a curly magnetic field
B units: T (Tesla) = kg s2A1