Transcript Electric Fields

Electric Fields
Montwood High School
AP Physics C
R. Casao
Electric Fields
• The space around every electric charge is
filled with an electric field which extends
through space.
• Every charge can exert forces on other
charges around it without actually being in
contact with the other charges and this force
This is an example of a field force and can be
determined using Coulomb’s law.
• The force that one charge exerts on another
can be describes as the interaction between
one charge and the electric field set up by the
other charge.
Electric Fields
• An electric field is a
vector quantity (has
both magnitude and
direction).
– Its strength
(magnitude) is
measured by its effect
on charges located in
the field.
– Small positive
charges are used as
“test” charges to
determine the
strength and direction
of the electric field
produced by a charge
at a point in space.
Electric Fields
• The direction of the electric field at any point
is the direction of the electrical force on a
small positive test charge placed at that point.
– If the charge that sets up the field is positive, the
electric field vector points away from the charge.
– If the charge that sets up the field is negative, the
electric field vector points toward that charge.
• The electric field vector E at a point in space
is defined as the electric force F acting on a
positive test charge placed at that point
divided by the magnitude of the test charge
qo:
F
E
qo
Electric Fields
• Note that E if the field produced by
another charge that acts on the test
charge qo; not the electric field
produced by qo.
• The vector E has the units of N/C.
• An electric field exists at a point if a test
charge placed at rest at that point
experiences an electric force.
• The electric field is said to exist at some
point regardless of whether or not a test
charge is located at that point.
Electric Fields
• When E = F/qo is applied, assume that
the test charge qo is small enough so
that it does not disturb the charge
distribution responsible for
producing the electric field at that
point.
• The strength of the electric
field is the same for all
points that are an equal
distance from the charge.
Electric Fields
• Consider a point charge Q located a distance r
from a point charge qo.
k  Qq o
– Coulomb’s law:
F
r2
– Electric field:
k  Q  qo k  Q
F
E
 2
 2
qo
r  qo
r
– The electric field at the position of qo is produced by
the charge Q.
• To determine the electric field due to a group of point
charges, determine the electric field vectors at the point
individually and then add them as vectors. The total
electric field due to a group pf charges equals the
vector sum of the electric fields of all the charges.
Charge Density
• If a charge Q is uniformly distributed throughout a
volume V, the charge per unit volume r is defined as:
Q
ρ
V
• Unit for r is C/m3.
• If a charge Q is uniformly distributed on a surface of
area A, the surface charge density s is defined as:
Q
σ
A
• Unit for s is C/m2.
• If a charge Q is uniformly distributed along a line of
length l, the linear charge density l is defined as:
• Unit for l is C/m.
Q
λ
l
Charge Density
• If the charge is not uniformly distributed
over a volume, surface, or line, we have
to express the charge densities as:
dQ
ρ
dV
dQ
σ
dA
dQ
λ
dl
where dQ is the amount of charge in a
small volume, surface, or length.
Electric Field Lines
• A convenient means of visualizing
electric field patterns is with with electric
field lines, also called lines of force.
• The electric field lines always point in the
direction of the force that would act on a
positive test charge qo.
– A positive charge is surrounded in all directions by
electric field lines that point away from the charge.
– A negative charge is surrounded in all directions by
electric field lines that point toward the charge.
• The electric field vector E is tangent to
the electric field line at each point.
Electric Field Lines
•The strength of the electric
field is indicated by the length
of the vectors.
•The electric field is greater
where the vectors are long
than it is where the vectors are
short.
Electric Field Lines
•The electric field is
stronger where the
electric field lines are
closer together;
weaker where the
lines are farther
apart.
Rules for Drawing Electric Field Lines
For any charge distribution:
1. The lines must begin on positive
charges and terminate on negative
charges, or at infinity in the case of
an excess of charge.
2. The number of lines drawn leaving a
positive charge or approaching a
negative charge is proportional to the
magnitude of the charge.
3. No two field lines can cross.
Electric Field Lines
•The charge on the
right is negative
because electric
lines of force go
into the charge;
the charge on the
left is positive
because electric
lines of force go
away from it.
•8 lines enter the
negative charge;
32 lines leave the
positive charge,
so the positive
charge is 4 times
greater than the
negative charge.
Electric Shielding
• When a car is struck by lightning, the people
inside the car are generally safe. The
electrons that strike a metal car repel each
other and spread out over the outer metallic
surface, finally discharging when additional
sparks move from the car’s body to the
ground.
• The electric field the charges set up outside
the car may be very large; the overall electric
field inside the car is almost zero.
• This is true of any charged conductor.
• The electric field inside a conductor is zero if
the charges on a conductor are not moving.
Electric Shielding
• The absence of an electric field inside a
conductor happens because electrons
within the conductor “settle down” and
stop moving only when the electric field
is zero, so the charges arrange
themselves to ensure a zero field with
the material.
• The material is attempting to attain
equilibrium, which occurs when the
arrengement of the charges produces a
field of zero inside the conductor.
Electric Shielding
• To shield an electric field, surround the
object with a conducting surface. The
free charges in the conducting surface
will arrange themselves on the surface
of the conductor in a way that all the
electric field contributions inside
cancel each other.
• Electronic components are often
encased in metal boxes and some
electrical cables have a metal covering
to shield them from all outside
electrical activity.
Electric Shielding
• Another way of determining if the electric field
inside the conductor will be zero is to count the
number of electric field lines coming into and
leaving the surface, if the number electric field
lines coming in equals the number of electric field
lines leaving the surface, the net electric field will
be zero.
MIT Visualizations
• URL: http://ocw.mit.edu/OcwWeb/Physics/8-02TSpring2005/Visualizations/Visualizations/electrostatics.htm
• Creating an Electric Field
• Destroying an Electric Field
• Attraction of Charges with Opposite Sign
• Repulsion of Charges with Same Sign
• The Electric Field of a Positive Charge
• Electric Field of a Moving Positive Charge
• Electric Field of a Moving Negative Charge
• Two Point Charges
• The Force on a Charge Moving Through an Electric Field
• The Electrostatic Zoo