For a uniformly charged spherical shell of
radius R and total charge Q, what is the electric
potential energy difference between a point on
the spherical shell and where . Assume .
Q
R
This is a cross-section view of the shell
The
total amount of work an
Amperes Law is
Here,
is the sum of the magnetic field component that is parallel to a closed
curve.
is the net current enclosed be the closed curve.
The Amperes law is only worth using under three circumstances:
1. When at every points on the closed curv
Consider the RLC circuit below. When the switch is at
position a, the capacitor is being charged, and when the
switch is in position b, the circuit is a RLC series circuit. If
the switch has been in position a for a long time, then at ,
the switch change
For
an inductor
and
so,
Also,
For
a Capacitor
and
so,
Also,
When an inductor is first connected to a DC power supply,
the back across the inductor is at its maximum value, and
the current through the inductor is zero, so the magnetic
field in the inducto
For
this circuit
, the current through the circuit is given by
,and the electric potential difference across the inductor is
given by
Here, is the electrical potential difference that was used to energize
the inductor, and .
So, the inductor acts like a
The equal sign in the equation does not imply causation but
correlation.
A changing magnetic flux DOES NOT cause a circulating
electric field to appear.
The equation tells us that a changing magnetic flux is
always ACCOMPANIED by a circulating electric f
Electric field outside a spherical ball example
Suppose you have a spherical ball of charge, Q, (Not a point
charge). What is outside this ball?
Electric field outside a spherical ball example
We can use Gauss Law to find outside this ball of charge by
im
PHYS 102
First Day Info
Welcome
Before starting with the material, there are
some organizational things we have to discuss
These slides will be posted in owlspace, you
dont need to write this down.
Syllabus
It is important that you read the syllabus
T
What is the goal of learning
electrostatics?
What is the goal of learning
electrostatics?
The goal is to be able to predict the force on an electric
charge if we place it in a region of space.
If we can systematically design what force is apply to
an elec
Faradays law of induction states that
Nature will always generate an to oppose changes in the
magnetic flux through the area enclosed by a conducting
loop.
Which can be written mathematically as
What exactly is this ?
In a DC circuit, the is the electric
Suppose we have a current going up the wire, lets find the force the
uniform magnetic field exerts on a straight segment of the wire that is
inside the uniform magnetic field.
The total
magnetic force the magnetic
field exerts on the segment of wire is
He
For a moving charge interacting with a uniform magnetic, where the velocity of the
charge particle is NOT parallel or antiparallel to the direction of the magnetic field.
Here is the radius of the circle in which the charge will move, and is the speed of
One problem with studying electricity is that we
usually cant see electricity, we can only observe
its effects.
What are some electric effects you have
observed?
The problem with studying electricity is that we
usually cant see electricity, we can only ob
While we cannot easily tell whether a plastic rod is
positively or negatively charge (had lost or gained
electrons), we can easily tell if it is charged.
A charged plastic rod can be used
1. To move other charged objects (either attract or repel)
2. To at
Once we know the electric potential due to a single point
charge, ,
we can find the electric potential due to any
arbitrary collection of charges.
Since electric potential is a scalar, the electric
potential at a point in space due to a collection
of char
We defined the electric potential within the
capacitor as
d
electric potential difference between the positive plate and the
negative plate of a capacitor is
The
d
Now, the electric potential within the capacitor
as defined by
has
d
Now, the electric pot
Recall that a bar-shape permanent magnet behaves like a
magnetic dipole.
If we place a bar magnet in the presence of a uniform
magnetic field as shown below. What would the bar magnet
do if the bar magnet is held in place at its center, but it is free
to
We will start our discussion of Electric Potential by
refreshing our memory about gravitational potential energy
near the surface of the Earth.
We will start our discussion of Electric Potential by
refreshing our memory about gravitational potential energ
We define an Electric Potential as
We define an Electric Potential as
So,
We define an Electric Potential as
So,
Since
then,
An electric potential exist at all position in space, regardless
if there is a charged object at any given position.
The only exa
The needle in a compass is a small, light weight magnet.
On Earth, all compass needles that are free to rotate on a
horizontal plane and are far from other magnets will line up
along the same direction.
When a compass needle settles on its preferred direc
Magnetic
field of a current loop example (off central axis)
Consider a thin circular wire loop of radius located in the
plane, and carrying a steady current , flowing counterclockwise as viewed from the positive z-axis. Calculate
the magnetic field at po
For an arbitrary shaped enclosure with a light source inside,
if we add up all the intensity at every points on the surface of the
enclosure and multiple that by the total surface area of the enclosure,
then we will get the total power output of the light
From
applying Faradays and Ampere-Maxwells Laws to a time varying
electric and magnetic field, we got
and
We can combine these two equations to get,
and
These two equations describe the propagation of electromagnetic waves
and
The solution of these two e
What happen to the electric energy of the charge as it goes
through the resistor?
+
_
You can picture the resistor as a region in the circuit where
the charge experiences a lot of collision as it falls to a lower
electric potential. Thus energy is loss to
When a wire is connected to a source of electric
potential difference like a battery or a charged
capacitor,
What do you think happen?
When a wire is connected to a source of electric potential difference
like a battery or a charged capacitor, Two things
Simple capacitor
example revisited
The spacing between the plates of a 1F capacitor is
0.05 mm. The plates are circular and equal in size. We
filled the space between the plates with titanium
dioxide which has a dielectric constant of .
What is the surfa
We
have considered an AC circuits where an AC voltage source is
connected in series with a resistor, an inductor, and a capacitor, such a
circuit exhibit resonance behavior. We can consider a RLC series
circuit as a band pass filter if we consider the vo
The set up of a transformer
gives us the relationship
which implies that the current flowing through
the secondary coil somehow influence the
current flow in the primary coil.
Another way to understand the relationship
is to ask,
How does the primary coil
We found earlier that for a parallel-plate capacitor, we have
and
and
d
Equipotential
Lines
The electric potential relative
to the negative plate, increases
linearly with distance from the
negative plate.
The electric field is constant
and points from th
is the equivalent capacitance of this series circuit.
In
general, for N capacitors in a series circuit
is the equivalent capacitance of the series circuit.
Another way that multiple capacitors can be connected
together in a circuit is for them to be in p