Download Physics 272: Electricity and Magnetism

Physics 272: Electricity and
Magnetism
Mark Palenik
Thursday June 14th
Topics
•
•
•
•
Finish up dipoles
Polarization of materials
Conductors
Charging/discharging
iclicker (not credit)
• An atom is placed in a UNIFORM electric field pointing
to the right and polarizes. What is the net force on the
atom?
𝐸
a) To the left
b) To the right
c) No net force
Force on a dipole (clicker, no credit)
• Net force on a dipole = Force on positive charge +
Force on negative charge
• 𝐹𝑛𝑒𝑡 = 𝐹𝑝𝑜𝑠 +𝐹𝑛𝑒𝑔 = 𝑞𝐸𝑝𝑜𝑠 − q𝐸𝑛𝑒𝑔 = 𝑞 𝐸𝑝𝑜𝑠 − 𝐸𝑛𝑒𝑔
• Assume we have a permanent dipole (not induced by
an external electric field) In which situation could this
force be non-zero?
a) It is placed in a uniform field 𝐸
b) A charge is placed along the perpendicular axis
+
c) A charge is placed along the parallel axis
d) Either b) or c)
+
Force on a point dipole
• We said𝐹𝑛𝑒𝑡 = 𝑞 𝐸𝑝𝑜𝑠 − 𝐸𝑛𝑒𝑔
• For a point dipole, P (dipole moment) is important, q is
meaningless
• Charges are distance s apart
𝑃
𝐸𝑝𝑜𝑠
𝑠
𝑠→0
𝐸(x+s)−𝐸(𝑥)
𝑃 lim
𝑠
𝑠→0
• 𝐹𝑛𝑒𝑡 = lim
− 𝐸𝑛𝑒𝑔
𝑃
𝑠→0 𝑠
= lim
𝐸(x + 𝑠) − 𝐸(𝑥) =
What does this look like? (think calculus)
s
It’s a
-
+
x
x+s
𝑑𝑦
derivative!
𝑑𝑥
=
𝑦 𝑥+ℎ −𝑦(𝑥)
ℎ
Dipoles respond to E field derivatives
• Force on a dipole = Dipole moment *
Derivitive of E field along dipole axis.
• E.g. if dipole is along x axis
• 𝐹𝑛𝑒𝑡 =
𝑑𝐸
𝑃
𝑑𝑥
• More formally we could write
• 𝐹𝑛𝑒𝑡 = 𝑃 ∙ 𝛻𝐸
Tensor
Polarization of materials
• Recall: Electric field lines push on positive
charges and pull negative charges
• Neutral atoms will polarize under the
influence of electric fields
• Materials are made of atoms, so materials will
polarize
– We call this INDUCED polarization
• Conductors and insulators behave differently
Electric fields and materials
• Plastic is an insulator: charges are not free to
flow
𝐸
Plastic sphere: each atom becomes
polarized, since the electrons
cannot flow
𝐸
• Metals are conductors
𝐸
Metal sphere, electrons can flow.
Sphere polarizes.
E=0
Protons DO NOT move
Polarization of a plastic sphere
• Draw the E field lines from the positive charge and the
polarization of this plastic sphere.
– Remember two things: 1) electrons are pushed opposite to
the direction of field lines
– 2) The field lines are NOT horizontal
+
Plastic Sphere
Non-external electric field
• The external electric field acting on a plastic sphere is
drawn below.
• Draw the electric field produced by the induced dipoles
below
𝐸
Note the field outside the
sphere does not oppose the
applied E
The field of the induced dipoles inside the sphere opposes the
applied field. As we will see, conductors are a special case.
Net field
• Superposition still applies
• One part of the field comes from the external,
applied field
• Another comes from the polarization field
• 𝐸𝑛𝑒𝑡 = 𝐸𝑒𝑥𝑡 + 𝐸𝑝𝑜𝑙
• 𝐸𝑝𝑜𝑙 is induced by the external field. This
happens in both conductors and insulators
Clicker Question
+
x
A
B
-
D
Plastic Block
C
What is the direction of the electric field at X due to the dipole?
Clicker Question
+
x
A
B
-
D
Plastic Block
C
What is the direction of the electric field at X due to the plastic
box?
Clicker Question
+
x
A
B
-
D
Plastic Block
C
What is the direction of the NET electric field at X?
Electric fields and metals
• Electrons are free to move inside of metals (nuclei are
still fixed, i.e. the atoms don’t move)
• What happens if I apply an external field to a piece of
metal?
• Will the electrons move? Will they ever stop moving?
If so, when?
Electric field in a conductor
•
•
•
•
•
At equilibrium, E inside any conductor is zero
Equilibrium is defined as when charges are static
If there is an E field, the charges will move
Therefore, in equilibrium, E=0 throughout the conductor
Charges arrange themselves so that they cancel the external E field
Reasons charges stop
a) E pushes charges toward
equilibrium
b) “Friction” like forces slow
electrons
𝐸
The electric field produced by the
sphere with this arrangement of
charges points left
Enet=0
Applied field points to the right.
The external applied field and
field produced by the sphere
cancel each other inside.
iClicker question: non-spherical
conductor
• Which best describes the NET electric field inside of this
triangular conductor with a positive charge nearby
Metal triangle
+
a) It points to the right, because of the positive charge
b) Non-zero because the conductor is not spherical, but not
necessarily to the right
c) Zero, because the triangle is a conductor
d) It points toward the positive charge
Charged conductor
• Where will excess charges go if I put them on a conductor?
– Keep in mind how charges affect each other.
++
+++
++
• When is the sphere in equilibrium?
In inject several positive
charges into the center of
a metal sphere, so it is no
longer neutral. Where do
they go?
Charged conductor and external
charge
• Qualitatively describe the net field of a charged, conducting
sphere and a point charge
Point charge
-
Conducting sphere
• Recall the field outside a uniformly charged sphere is the
same as that of a point charge?
• Is the total field the same as the sum of the field of the
individual objects?
– In what circumstances might this or might this not be true?
Discharging by contact
On approach: body
polarizes
On contact: charge
redistributes over
larger surface
Charging by induction
What is a conductor?
• Charges in conductors can be mobile.
• Either electrons or ions can flow
• In metals, there is a well ordered crystal structure,
many close energy levels: a sea of electrons that can
flow
Gray is the electron sea.
The red +’s are the positive
cores
What is a conductor 2
• In ionic solutions, molecules have split into + and –
ions, which can flow in solution. E.g. NaCl becomes
Na+ and Cl-