Transcript Electric Field Lines - universityscience.net

How do most objects interact with each other?
•Electric Charge (q or Q)
–An intrinsic property of matter (as is mass)
–S.I. unit: coulombs (C), (also: μC)
–Two types (+) or (-): add algebraically to give a net
charge.
–Like charges repel; unlike charges attract.
–Coulomb’s Law: The force between two charges (q1) and
𝑘 𝑞1 𝑞2
q2) separated by a distance r is: 𝐹𝑒 =
.
2
𝑟
– k is Coulomb’s constant: k = 9 x 109 Nm2/C2
–Force by q1 on q2 is equal and opposite to the force by
q2 on q1.
More about Charge.
• Quantization of charge (e): charge comes in
discrete amounts of 𝑒 = 1.6x10-19C
• 𝑒 is the “elementary charge”; we always treat 𝒆 as
positive.
• Electrons have a charge of −𝑒
• Protons have a charge of +𝑒 and about 2000 times
the mass of electrons.
• Conservation of charge: In any reaction, net charge
remains the same. (Is this different from
conservation of mass?)
Examples
• Book sitting on a table
• Pushing off
– A hard wall
– A soft wall
– Electric Force is a measure of hardness in repulsion.
• Sodium Metal vs. Aluminum Metal.
• Potassium Metal vs. Sodium Metal.
– Electric Force is a measure of hardness in attraction.
• What happens if we hold a
– Negatively charged rod held near a neutral atom?
– Positively charged rod held near a neutral atom?
• Both atoms are said to have become polarized and
move towards the charged rods. We have net attraction
in BOTH cases.
Using Coulomb’s Law
1. A charge (Q) of +2µC is fixed in the ground.
A charge (q) of +3µC having a mass of 0.24 kg
is held 0.15m directly above the fixed charge
and released.
How does the charge q move?
Give the magnitude and direction of its
acceleration.
Use (g = 10 m/s2 and k = 9 × 109 Nm2/C2)
Using Coulomb’s Law (cont’d)
2. Two protons are separated by 5×10-15m.
a. Calculate the force on one proton due to the
other. (qp= + e = 1.6×10-19 C). Does the force
seem small or large as felt by:
a person?
a fly? a proton?
b. Calculate the acceleration of the proton. Is
this a large number? (mp= 1.67×10-27 kg)
Using Coulomb’s Law (cont’d)
3. Three charges (q1 and q3 are fixed):
q1 = -86 µC at (52 cm, 0)
q2 = +50 µC at (0, 0)
q3 = +65 µC at (0,30 cm)
What is the net force on q2? (magnitude and
direction)
What is its acceleration if it has a mass
of 0.5 kg?
Electrical Properties of Materials
• Conductors: Outer electrons can
move nearly freely through the
material. (What is it about metallic
bonding that allows this?)
• Insulators: Outer electrons are
bound tightly to the atoms. Cannot
move freely.
Electrical Properties of Materials (cont’d)
• Semiconductors: Outer electrons are bound,
but not so tightly. (e.g. silicon, germanium)
– Can be made to conduct electricity in very
controlled ways.
– Doping: impurities to increase or decrease
electrons in crystal structure (e.g. transistors)
– Photoelectric Effect: electrons can be
energized by absorbing light ot leave their
atoms and travel through the material. (e.g.
photocells)
How can charge be transferred
between objects?
1. Friction
•
•
•
Electrons transferred by rubbing.
Rubbing plastic with fur; fur loses electrons.
Rubbing glass with silk; silk gains electrons.
2. Induction (In Insulators)
•
•
•
A charged object causes electrons to move in a
neutral object.
Atoms become polarized; they turn into dipoles.
Charged rod (+) or (-) near a neutral object; what
happens?
How can charge be transferred
between objects? (cont’d)
3. Conduction
• Electrons can move freely through some
materials, called conductors.
• Conductors can be charged directly through
contact with charged objects (not friction).
• Conductors can be charged through induction
 Electrons move freely to one side or another;
object as a whole becomes polarized.
Van de Graf Generator
• Device to concentrate positive
charge on a conducting sphere.
• Operation:
– Lower roller (G) rubs electrons (e- )
off belt.
– Belt becomes (+)
– (+) belt attracts e- from brush (B),
bleeding them off the conducting
sphere (A) and neutralizing belt.
– Neutralized Belt travels back to
lower roller.
– Sphere (A) becomes (+) more and
more.
Electric Field (E)
• How does one charge “know” that another charge
is there? (“Action at a distance”).
• A charge actually changes the space around it; a
force field is caused.
• Other charges interact with this “Electric Field”.
• E is a VECTOR:
The direction of E at a point is in the same direction
that a small positive point charge (qT) would move if
placed at that point. (BY DEFINITION)
The magnitude of E at a point equals the Force
on qT divided by qT. E = Fe/qT (BY DEFINITION)
Advantages of the E-Field
• The Electric fields caused by several charges add up
as vectors.
• For a system of charges or objects:
– Find the resultant (net) E-Field
– Now you can easily find the force on any charge (q) you
place in the system: Fe= q E
– If q is (+), then Fe and E are in the same direction,
otherwise they are opposite to each other.
• If you change q, you don’t need to recalculate the
E-field.
• The E-field is physical; energy is actually stored in
space.
Using the E-Field
1. A charge of q = +4.0 µC feels a force of 2.0N to
the right. What are the magnitude and
direction of the E-Field?
2. A charge of q = -8.0µC feels a force of 2.0N to
the right. What are the magnitude and
direction of the E-Field?
Using the E-field
3. A charge of (q= +6µC) and mass (m=2×10-3kg) is at
the origin and moving in the +x-direction with an
initial speed (vi=2×102m/s). A uniform E-field
(with magnitude: E=3×105N/C) acts in the
negative x-direction.
a.
b.
c.
d.
Find the force on the charge.
Find the acceleration of the charge.
Find the maximum value of +x reached by the charge.
Find the time for the charge to return to its start
point.
Using the E-field (cont’d)
4. A pendulum with: charge (+Q)
and mass (m) is in equilibrium
in a uniform E-field applied in
the +x-direction.
In
terms of Q, m, and θ,
a.
Find the magnitude of the Efield.
b. Find the tension in the string.
c. Describe the motion of the ball if
the string is cut. (Be as specific
as you can.)
Using the E-field (cont’d)
5. How can we find the E-field due to a point
charge Q at a point (P), a distance (r) from
Q?
Find magnitude of E at the point P.
Show direction of E at P if Q is (+)
Show direction of E at P if Q is (-)
Electric Field Lines
• Used to visualize an
electric field’s
– Direction: Directed
path along which a
positive test charge
would move.
– Magnitude:
Proportional to the
number of field lines
coming through an
area (line density).
Drawing Electric Field Lines
To draw the electric field lines for a single charge
1. Draw lines directed away from (+) charges.
2. Draw lines directed towards (-) charges.
3. The number of lines entering or leaving the
charge is proportional to the amount of
charge.
4. Examples to do: Using 4 lines for a (+1 C)
charge, draw the field lines for:
a. +1C charge, +2C charge, -1C charge, -2C
charge.
Drawing Electric Field Lines (cont’d)
To draw electric field lines for a system of
charges:
1. Draw field lines near each charge in the
system.
2. Connect field lines smoothly between
(+) and (-) charges.
3. Field lines between like charges can go to
infinity.
4. Draw field lines perpendicular (normal) to
conducting surfaces (why?).
Examples
1. Dipole (+ -)
2. Two (+) charges (+ +)
3. Quadrupole
+
+
4. Oppositely charged plates that are close
together.(*Important*)
Check answers at Electric Field Applet
How does a Conductor behave in an E-Field?
• In electrostatics, charges don’t move. (Fields due
to stationary charges are called electrostatic
fields.)
• Recall what happens when we put a charged rod
near a conductor:
– Transient current
– Polarization of entire object
– Electrons moved so as to cancel the E-field inside the
conductor. (Why must this be so?)
• Excess charges move to surface and distribute
themselves out of mutual repulsion.
• And so ....
How does an E-field behave in a Conductor?
• No electrostatic field can exist in the material of
a conductor.
• At the surface of a charged conductor:
– E-field is perpendicular to the surface.
– Component tangential to the surface is zero.
– Higher concentrations of charge occur at surfaces of
higher curvature.
• In an empty cavity within a conductor
– E-field is zero
– Region is shielded from any external charges.
Charge densities at curved surfaces
 On flat surfaces of low curvature,
repulsive forces are directed mostly
parallel to surface, keeping charges
further apart.
 On highly curved surfaces,
parallel components of the repulsive
forces are smaller, allowing charges
to be closer together.
Result: Strong E-fields near highly
curved surfaces. (Ex: Lightning
Rods)
Electric Field Lines near a Conductor
Conductor in an E-field
(summary)
Field is normal to surface
Field is ZERO in
an empty cavity.
Charge concentrates
at high curvature.
Field is NOT zero in a
cavity containing charge.
How can we describe the difficulty of moving mass or
charge without regard to how much there is to move?
• Gravitation: We need to do work to lift material
against a gravitational field. How can we describe
how hard it is to lift the material without regard to
how much there is?
 Think about the Work you have to do per unit mass.
• Electric Case:
– Think about the Work we have to do per unit charge:
𝑊
𝑉=
= change in Electric P.E. /charge
𝑞
Units: joules per Coulomb = volt
– Recall: Work changes Energy of a system and is equal
to the change in energy that it causes.
Visual Example: Topographical Maps
• Topo map: maps contours or lines of equal
gravitational potential.
• No work is done to move objects along these
lines.
• Moving across lines requires work
– Closely spaced lines indicates steepness.
– Steepness indicates the strength of the field in the
direction of your movement.
(e.g. “field strength” here would be analogous to an an
inclined plane: g sinθ; direction of fall would be down
the plane.)
Topo map
Electric Potential and Charged Material
• E-field direction specifies
region of high V to region
of low V.
• (+) charges fall to:
___________ potential
_________ potential energy
• (-) charges fall to:
___________ potential
_________ potential energy
+
|
|
(b)
High V
E 
|
|
(a)
Low V
ΔPEe = q ΔV
Some Examples
1. An electron is accelerated across a
voltage of 5000 volts between two
plates.
a. What is the change in potential energy of the
electron?
b. What is the work done on the electron by the
E-field between the two plates?
c. What speed does the electron attain?
d. Who works with these kinds of problems?
e. What is an “electron-volt (eV)”?
The Electron Volt
• The amount of work needed to push an electron
across a potential difference of 1 volt.
• Allows MUCH easier calculations of energies.
• Allows MUCH easier grading of the calculations.
• Use them when charges are given in units of “e”.
• 1 eV = (1.60×10-19C)(1 J/C) = 1.60×10-19J
• Notice: instead of multiplying voltage by the electronic
charge in coulombs, you just put an “e” in front of it.
• If you’re asked for speeds; you’re back to S.I. units.
Examples (cont’d)
2. Two plates are charged to a voltage 50V. If their
separation is 5.0 cm, what is the E-field
between them?
The E-field is uniform
+
between the plates.
|
|
|
|
+50 V
|
|
|
|
0V
| d = 5 cm |
Visualizing Electric Potential
• Draw Equipotentials: Lines along which
the electric potential is constant.
• Similar to contours on a topo map.
• Questions
– How would you calculate the work done in
moving a charge along an equipotential?
– How are equipotentials related to electric
field lines?
They are perpendicular to each
other at every point.
Mapping Equipotentials
• What do equipotentials look like for
– A point charge?
– A dipole?
– Two like charges?
– Applet as before: Electric Field Applet
• For a charge distribution, how could you
experimentally map
– Equipotentials?
– Electric field lines?
• What is the gravitational equivalent for a map of
equipotentials?