Download revision lecture.

SEF006 (2017)
Page 1
REVISION LECTURE.
Gravitational Field.
The escape velocity is the minimum speed needed for an object to escape from a massive
body.
The gravitational potential is equal to the work per unit mass that would be needed to move
the object from infinity to the location of the object.
According to above definitions and the energy conservation law
Ekin + Epot = 0,
where
2
Ekin = mvesc
/2 and Epot = mV.
Hence
2
vesc
/2 + V = 0, and vesc =
√
−2V .
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SEF006 (2017)
Electric Field.
Coulomb’s law states: The force is proportional to product of charges and inversely proportional to the square of the distance separating them. This law is applicable to point charges.
Electric flux is the measure of flow of the electric field through a given area. Electric flux is
proportional to the number of electric field lines going through a normally perpendicular surface.
If the electric field is uniform, the electric flux passing through a surface S is ΦE = ES.
The the flux of the electric field trough a sphere of radius R around a point charge Q is
ΦE = ES =
Q
Q
× 4πr2 = ,
2
4πε0 r
ε0
hence, ΦE is proportional to Q and does not depend on the radius of the sphere.
Attractive Coulomb’s force between the proton and the electron is
F =
e2
,
4πε0 r2
where e is the electric charge of electron.
If there are N protons in the nucleus and the electron moves around the nucleus along a
circular orbit of radius r, the acceleration of electron is
a=
N e2
v2
= F N/me =
,
r
4πme ε0 r2
where me is the mass of electron and
s
v=
N e2
.
4πε0 r
SEF006 (2017)
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Magnetic field.
If electric charge Q moves with velocity v at right angle to some magnetic field of strength B,
the charge experiences a force, F = BQv.
Electron moving with velocity v along a circular orbit of radius r corresponds to a currant
I=
ev
2πr
in circular conductor of radius r and, hence, generates magnetic field
B=
µ0 I
µ0 ev
= 2 2.
2πr
4π r
Electromagnetic induction.
Electromagnetic induction is the production of an electromotive force (i.e., voltage) across an
electrical conductor due to its dynamic interaction with a magnetic field.
Electromotive force, e. m. f. (denoted here as ε) and measured in volts, V), is the voltage
developed by any source of electrical energy such as a battery or dynamo. It is generally defined
as the electrical potential for a source in a circuit. The word ”force” in this case is not used to
mean mechanical force, measured in newtons, N, but a potential, or energy per unit of charge,
measured in volts.
The flux of magnetic field (denoted here as B ) through a surface is the surface integral of the
normal component of the magnetic field B passing through that surface. The unit of magnetic
flux is the weber (Wb).
The Faraday’s law states: The induced electromotive force in any closed circuit is equal to the
negative of the time rate of change of the magnetic flux enclosed by the circuit.
The Lenz’s law says: The direction of current induced in a conductor by a changing magnetic
field due to Faraday’s law of induction will be such that it will create a field that opposes the
change that produced it. Lenz’s law is shown by the negative sign in Faraday’s law of induction:
ε=–
dΦB
.
dt
The minus, –, in the Faraday’s law means that the e.m.f. creates a current I and magnetic field
B that oppose the change in flux. This is Lenz’ law.
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SEF006 (2017)
Simple Harmonic Oscillation (SHO).
If the force acting on a body is proportional to the displacement and has the opposite direction
the motion of the body is called SHO.
In orther words, the SHO is described by the following equation:
ẍ = −ω 2 x and F (x) = −mω 2 x.
The period of SHO is
T = 2π/ω,
Displacement x depends on time t as
x = A sin ωt,
(1)
Differentiating above equation one obtains
p
p
v = Aω cos ωt = ±Aω 1 − sin2 ωt = ±ω A2 − A2 sin2 ωt.
Waves.
Transverse wave is such a wave in which direction of oscillations is perpendicular to the direction of the propagation of the wave. Transverse waves can be polarized, for example, electromagnetic wave passed through crystal.
Running waves transfer energy from one point to another, while standing waves don’t. Example
of standing wave: Oscillations of wire with fixed ends.
SEF006 (2017)
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Diffraction grating.
A high number of parallel slits arranged closely together is called a diffraction grating. In such
an arrangement the peaks appear as sharp thin lines (principal maxima). Diffraction gratings
(DGs) are used to measure wavelengths with high accuracy.
There are two types of DGs:
1) transmission DGs - black parallel lines on transparent plastic or glass,
2) reflection DGs - a reflective surface between black parallel lines.
The location of each peak with number m is given by
d sin θm = mλ,
where d is the spacing between two adjacent slits.
Taking into account that sin θm ≤ 1 we obtain
m≤
d
.
λ
If λ ≈ 500 nm the light is green light, if λ > 600 nm the light is red.
Slits.
Two plane monochromatic electromagnetic waves pass through two identical slits of the same
width and are seen on a screen which is located in front of the slits.... (See the lecture notes and
the book to find a problem which is related to the above sentence).