Download Forces and Fields.

Topic 6: Fields and forces
6.1 Gravitational force and field
State Newton’s universal law of
gravitation.
Students should be aware that the
masses in the force law are point
masses. The force between two
spherical masses whose separation
is large compared to their radii
is the same as if the two spheres
were point masses with their
masses concentrated at the centers
of the spheres.
Newton’s laws of gravitation
Anything with mass attracts
anything else with mass. The size
of that attraction is given by my
Law of Gravitation:
State Newton’s universal law of
gravitation.
Newton 1642-1727
F = Gm1m2
r2
…where m1 and m2 are the masses of the two objects (in kg), r
is the distance between them (in m) and G is “The Universal
Gravitational Constant” (= 6.67 x 10-11 Nm2kg-2).
Cavendish measurement of G
Click to play
Inverse square law
What holds the planet in orbit?
Free Body Force Diagrams revision
The Earth attracts the man and
the man attracts the Earth – a
Newton III pair of forces where
both are gravitational.
A uniform gravitational field is one where the field
lines are always the same distance apart - this is
almost exactly true close to the Earth's surface
(Figure 1(a)).
However if we move back and look at the planet from a
distance the field lines clearly radiate outwards (Figure
1(b)), getting further apart as the distance from the
Earth increases.
When viewed from an even greater distance the
complete field can be seen (Figure 1(c)).
radial field - the field
Such a field is called a
intensity (g) decreasing with distance.
Diagram 1(d) shows the distortion of the gravitational
field lines by high- density rock.
Gravitational Field Strength
Consider a man on the Earth:
Derive an expression for gravitational field strength
at the surface of a planet, assuming that all its mass
is concentrated at its
centre.
Man’s weight = mg
BUT we know that this is equal to his
gravitational attraction, so…
GMm = mg
r2
Therefore:
GM = g
r2
(this is a vector quantity)
Gravitational Field Strength
Define gravitational field strength.
Definition: Force, act, point, unit
mass.
Write a definition of gravitational
field strength
Determine the gravitational field
due to one or more point masses.
Derive an expression for gravitational field
strength at the surface of a planet, assuming
that all its mass is concentrated at its
centre.
6.2 Electric force and field
State that there are two types of
electric charge.
Static Electricity
+
+
-
-
+
-
-
-
-
-
-
-
Conservation of charge
State and apply the law of
conservation of charge.
The law of conservation of charge states…………….
One of the fundamental laws of Physics is that charge can never be
created or destroyed. Charge is always conserved in any reaction. A
simple example of this is the rubbing of a polythene strip with a duster.
Initially the strip and the dusted were uncharged but after rubbing the strip
gains a net negative charge and the duster gains an equal amount of
positive charge – the total charge in the process has been conserved.
Conductors and insulators.
Describe and explain the
difference in the electrical
properties of conductors and
insulators.
The difference between conductors and
insulators is………………
In a conductor, the conduction and valence bands overlap. This allows the
valence electrons to easily move along the conduction band giving the
material low electrical resistance.
In insulators, there is a large forbidden energy band, which makes it difficult
for valence electrons to move into the conduction band giving the material a
high electrical resistance.
In semiconductors, the forbidden energy band is not too wide. Under certain
conditions, electrons in the valence band can gain sufficient energy to cross
the gap. This reduces the electrical resistance of the material.
Coulomb’s law
State Coulomb’s law.
Students should be aware that the charges
in the force law are point charges.
Coulomb’s Law
Like gravity, electrostatic force is one of the
four fundamental forces. The equation looks
pretty similar too…
Coulomb’s Law
F = kQ1Q2
r2
Charles Coulomb
1736-1806
…where k = 9.0 x 109 Nm2C-2 (the “Coulomb Law Constant”).
This comes from k = 1/4πε0 …
…where ε0 = permittivity of free space (i.e. 8.85 x 10-12 Fm-1).
Electric field of a point charge
Define electric field strength.
Write a definition of
electric field strength
Students should understand the
concept of a test charge.
Determine the electric field
strength due to one or more
point charges.
Electric field patterns
Draw the electric field patterns for
different charge configurations.
These include the fields due to the
following charge configurations:
a point charge, a charged sphere,
two point charges, and oppositely
charged parallel plates. The latter
includes the edge effect. Students
should understand what is meant
by radial field.
How do we predict the shape of
a field?
• Imagine that you have a unit positive test
charge.
• Place it in a point in the field.
• Sketch the path it would take.
• Repeat this many times until you have
enough field lines
• The “density” of the lines represents the
strength of the field.
Point charge
+
Sphere
Positive or negative
2 Point charges
+
+
2 Point charges
+
-
Parallel plates
+
_
Edge effects
Electric Fields
Electric field strength E = F
q
Let’s compare this to
Coulomb’s Law:
(this is a bit like gravitional
field strength g = F/m)
Coulomb’s Law
Putting these equations together gives us…
Electric field strength E = kQ
(in NC-1)
r2
F = kQq
r2
Electrostatic force and circular motion
Consider an electron orbiting a nucleus in a hydrogen atom:
e
Q. If the mass of an electron is
9.1x10-31kg and the distance to the
proton is 0.11nm how fast is the
electron going?
p
Using mv2 = kQq we get v = 1.5x106 ms-1
r
r2
A practical example
Consider a charged polythene strip and a metal ball:
+ - +
+ - +
- -
-
-
-
-
-
Fields applet
Field for a point charge
Click to play
Electric dipole
Click to play
Falstad.com
Falstad.com
Electric fields around a point charge
http://www.falstad.com/emstatic/
2 Charged
Spheres
Draw the edge effects for the parallel plate
Uniform electric fields
Consider two charged plates:
Now consider a point charge:
Work done
= QV
Q
For an electron,
eV = ½mv2
+
V
-
Visualising the fields
Hyperlink
6.3 Magnetic force and field
Permanent magnets and
domains
State that moving charges give rise to magnetic fields.
Hyperlink
Draw magnetic field patterns due
to currents.
These include the fields due to currents in a
straight wire, a flat circular coil and a solenoid.
Field around a wire
Click to play
Field around a loop
Click to play
B field for a loop
Click to play
Field patterns
Left hand Motor Rule
Determine the direction of the force
on a current-carrying conductor in a
magnetic field.
Fleming's left- hand rule
Current-carrying wire in a magnetic field
N
F = Force
B=
Magnetic
field
I = Current
S
Q. Where will this wire go?
Comparing magnets and solenoids
Magnet:
N
Solenoid:
S
Magnetic Field around a Solenoid
Forces on a loop
Click to play
Electric motor
Click to play
Hyperlink
Magnetic Flux Density
Clearly, the size of the force on this wire depends on three
things:
1. The strength of the magnetic field
2. The current in the wire
3. The length of the wire (in the field)
These three things are related by the simple formula…
B is called “magnetic flux density” and is measured in Teslas (=
1NA-1m-1). By definition, a magnetic flux density of 1T
produces a force of 1N on a 1m long wire with a current of 1A.
Hamper HL page 208 Q’s 37,38 SL Page 141 Q’s 8,9.
Determine the direction of the force on
a charge moving in a magnetic field.
Force on a charged particle
Define the magnitude and direction of
a magnetic field.
A magnetic flux density of 1T produces a force of 1N on a 1m
long wire with a current of 1A.
Recall:
+
+
Circular paths
2 protons, 2 neutrons,
therefore charge = +2
-
1 electron, therefore
charge = -1
Because of this charge, they will be deflected by magnetic
fields:









These paths are circular, so Bqv =
mv2/r,
or
r =mv
Bq
Circular paths
if angle = 90° the path is circular
if 0 < angle < 90° the path is a helix.
How do you work out which bit is circular?