Transcript AP Physics II.A

AP Physics III.A
Electrostatics
18.1 Origin of Electricity
The Fundamental Charge (Robert
Millikan and his oil drop
experiment)
Ex. How many electrons are in two Coulombs of negative charge?
18.2 Charged Objects and
Electric Force
Law of Conservation of Charge –
during any one process, net
electrical charge of an isolated
system remains constant.
Ex. Two identical isolated conducting spheres, one with charge
-6 μC and another with net charge +2 μC are allowed to touch.
If the two spheres have the same net charge after touching,
what is the net charge on each sphere?
Attractions and repulsions
18.3 Conductors and Insulators
18.4 Charging by Induction and
Conduction (also known as, “I
wish I had a decent
electroscope”)
Charging by Conduction
Charging by Induction
Induced charge on an insulator
18.5 (Charles De) Coulomb’s
Law
“Hmm, this looks like something
I’ve seen before”
Ex. An electron “orbits” the proton of a hydrogen atom at an
average distance of 0.53 EE 10-10 m. What is the force that the
proton exerts on the electron? What is the velocity of the electron
for a circular orbit?
Ex. Two charges exert electrical force F on each other. If
the magnitude of each charge is doubled and the distance
between them is halved, what is the force F′ on each charge
in terms of F?
Electric forces and vectors
Ex. Three Charges in a Line
Ex. Three Charges in a Plane
III.A.2 Electric Fields and
Electric Potential
A mass in a gravitational field
Charges experience an electrostatic
force due to the presence of other
charges
An electric field is a vector that
has a direction that the force exerts
on a positive test charge.
Some examples
Ex. Find the electric force on a proton placed in an electric field
of 2.0 EE 4 N/C that is directed along the positive x-axis.
Electric fields are vectors. The
net electric field at a point in
space can be determined by
considering the contributions of
each charged object and adding
them together as vectors.
Ex. Electric Field Between Two Point Charges. Two point charges
are separated by a distance of 0.100 m. One has a charge of –25.0
μC and the other 50.0 μC . a) What is the magnitude and direction
of the electric field at point P between them 0.020 m from the
negative charge? b) If an electron is placed at rest at P, what is
the magnitude and direction of its initial acceleration?
Symmetry and the electric field.
Electric Field Lines
Notes about field lines
• Electric field lines originate on positive charges
and terminate on negative charges
• The density of the field lines per unit area shows
the strength of the field (uniform and non-uniform
fields)
• Electric field lines are perpendicular to the surface
of a charged object
• The direction of the field is tangent to any point
on the field line
• Electric field lines do not cross (Why not?)
Field lines around positive and
negative charges
Field lines between plates of a
capacitor.
Field lines between two dipoles
Field lines between two identical
charges
Electric Potential Energy
Work done on a charge in a uniform
electric field
Muy importante – the
displacement of the charge is in
the direction of the electric
field.
Let’s clarify but not overemphasize
the signs
Electric Potential Difference
Let’s look at “gravitational
potential” first
So change in electric potential is . . .
Electric potential decreases or
increases not because the field exerts
any more or less force (the field is
uniform – like gravity near the
Earth’s surface). V changes because
of distance. A charge released in the
field, traveling a greater distance
converts more of its Ue to K (like
dropping an object from a greater
height).
Everyday examples
Potential (and therefore potential
difference) is scalar (this will
simplify some things).
Summary
• Electric potential energy – energy a charge
has because of its potential in an electric
field (so far the field is uniform)
• Electric potential – electric potential energy
per unit charge
• Potential difference – change in electric
potential
Another formula “Ed has potential”
V = −Ed (only true for a uniform
electric field)
Ex. In the figure shown, the work done on a 2.0 µ C charge by the
electric field from A to B is 5.0 EE -5 J. What is the change in
electric potential energy and the potential difference?
A·
B·
Worth noting: a positive charge
accelerates from a higher potential to
lower potential. A negative charge
accelerates from lower potential to
higher potentials.
Conservation of Energy – yep,
here it is again with electrical
potential energy in the picture
Ex. A proton is released in a uniform electric field with a
magnitude of 8.0 EE 4 V/m directed along the positive x-axis. The
proton undergoes a displacement of 0.50 m in the direction of the
field. a) Find the change in electrical potential energy. b) Find the
potential difference. c) Find the speed if the proton starts from
rest.
Ex. A particle with mass of 1.8 EE -5 kg and a charge of 3.0 EE 5 C is released from rest at point A and accelerates horizontally
to point B. The only force on the particle is the force from the
electric field and the electric potential at A is 25 V greater than
the potential at B. What is the velocity of the particle at B?
Electric Potential Due to a Point
Charge (requires calculus, sorry no
proof today. Take AP Physics C and I
will prove it for you next year.)
Important to use the signs when
finding the potential of a point
charge. Graphically – potential from
a positive charge is positive and
decreases to zero at infinity.
Potential from a negative charge is
negative and increases towards zero
at infinity.
Electric Potential for a Pair of Point
Charges
Ex. A 5.0 µC charge is at the origin and a -2.0 µC charge is on
the x-axis at (3.0, 0) m. a) If the electric potential is zero at
infinity, find the total electric potential due to the charges at P,
with coordinates (0, 4.0) m. b) How much work is required to
bring a third charge of 4.0 µC from infinity to P?
Ex. How many places are there on the line below where the
potential is zero? Where is (are) these locations?
2q
-q
Ex. Potential energy for a group of charges
Equipotential Lines (or surfaces)