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PH5 Notes

Capacitance

𝐶 =

𝑄
𝑉

C = Capacitance (F)
Q = Charge (C)
V = Potential Difference (V)

For a parallel plate capacitor with no
dielectric:
𝜀' 𝐴
𝐶 =
𝑑
C = Capacitance (F)
𝜀' = Permittivity of free space (𝐹𝑚 -
...

𝐶0

For capacitors in parallel:
𝐶 = 𝐶
...
= Capacitance of capacitor 1 (F)
𝐶0 = Capacitance of capacitor 2 (F)

C = Total capacitance (F)
𝐶
...

𝑄 = 𝑄' 𝑒

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89

Q= Charge (C)
𝑄' = Charge at t=0 (C)
t = Time (s)
R = Resistance (Ω)

𝐼 = 𝐼' 𝑒

-74
89

I= Current (A)
𝐼' = Current at t=0 (A)
t = Time (s)
R = Resistance (Ω)

𝑉 = 𝑉' 𝑒

-74
89

V= Potential difference (V)
𝑉' = Potential difference at t=0 (V)
t = Time (s)
R = Resistance (Ω)

PH5 Notes

B-Fields

𝐵 =

𝐹
𝐼𝑙

B= Magnetic flux density (T)
F = Force on the wire (N)
I = Current through the wire (A)
l = Length of the wire (m)

For a moving charge in a magnetic field:
𝐹 = 𝐵𝑞𝑣 sin 𝜃
F = Force on the wire (N)
B= Magnetic flux density (T)
q = Charge (C)
v = Velocity of the moving charge (𝑚𝑠 -
...


t
d
B-Field into Hall Probe
𝑛 =

𝐼𝐵
𝑉F 𝑡𝑒

n = Number of free electrons
I = Current (A)
B = Magnetic flux density (T)
𝑉F = Hall voltage (V)
t = Width of Hall probe (m)
d = Height of Hall probe (m)

Current

To investigate steady
magnetic fields:
When the Hall probe is placed
in the magnetic field a p
...

that is directly proportional to
the magnetic flux density is
produced across the Hall
probe at right angles to the
direction of the current
...
)
𝑉F = Hall voltage (V)
B = Magnetic flux density (T)
d = Height of Hall probe (m)

PH5 Notes
You may have to prove the Hall voltage equation:
𝐼 = 𝑛𝐴𝑣𝑒
𝑣 =

𝐼
𝑛𝐴𝑒

𝑉F
𝐼
=
𝐵𝑑
𝑛𝐴𝑒

𝑛=

𝐼𝐵𝑑
𝑉F 𝐴𝑒

𝑛=

𝐼𝐵𝑑
𝑉F 𝑡𝑑𝑒

𝑛=

𝐼𝐵
𝑉F 𝑡𝑒

Since A = t x d

PH5 Notes
Charged particles moving in a magnetic field

Magnetic Field Diagrams:
For a long straight wire:

For a long straight wire:
𝜇' 𝐼
𝐵 =
2𝜋𝑎
B = Magnetic flux density (T)
𝜇' = Permeability of free space (𝐻𝑚-
...

Where the current goes in, it’s
South
...


Adding an iron core increases the field strength
...
)
n = Number of turns per unit length
I = Current (A)

For 2 parallel wires

When two wires carry a current, they will exert forces on one another, the
reasons for this are:
- The top wire has a magnetic field
...

Currents in opposite directions repel
...
6 x 10-19 J

Linear accelerator (Linac)
The acceleration is provided by an electric field
...

The tubes get longer so that as the particles
accelerate, the time spent in each tube
remains the same
...
c power source
The potential difference is synchronised so that the charged particle is inside
a tube as the potential difference changes direction
...

The charged particle accelerates
in the gap between the dees,
travelling in a spiral path
...

The frequency is kept fixed
...


𝑓 =

𝐵𝑞
2𝜋𝑚

f = Frequency (Hz)
B = Magnetic Flux Density (T)
q = Charge (C)
m = Mass of the particle (kg)

Synchotron
The speed increase is provided by an alternating potential
difference
...

Acceleration occurs 4 times per orbit in the gaps between
oppositely charged tubes
...
c power source

The path remains constant (no spiralling) so the B-field
increases in strength as the speed of the particle increases
...
c
...

For particle accelerators with circular
motion:

𝐵 =

𝑚𝑣
𝑞𝑟

B = Magnetic Flux Density (T)
m = Mass of the particle (kg)
v = Velocity (ms-1)
q = Charge (C)
r = Radius (m)

PH5 Notes

Electromagnetic Induction

φ = Magnetic flux (Wb)
A = Surface area (m2)
B = Magnetic flux density (T)
θ = Angle between the magnetic field and the
normal to the plane of the coil

N = Number of turns in a coil
φ = Magnetic flux (Wb)
B = Magnetic flux density (T)
A = Surface area (m2)

E = EMF induced (V)
N = Number of turns in a coil
φ = Magnetic flux (Wb)
t = Time (s)

For a linear conductor moving at right angles to a B-field, you use the
equations

PH5 Notes
A Rotating Coil in a Magnetic Field
Flux Density
The induced emf is proportional to the
strength of the B-field
...

Coil Area
The coil area is proportional to the
induced emf, because a larger area
results in a larger magnetic flux linkage
for the coil
...


𝑉
...
T
...
m
...
value is related to the energy dissipated per cycle
𝑉'
𝑉
𝑉
...
S
...
=
√2
= U
𝑁

Vrms = Root-mean-square potential
difference (V)

Vrms = Root-mean-square potential
difference (V)
V0 = Peak potential difference (V)

\ = 𝑉𝐼
𝑃

𝐼Q
...
T
...
m
...
Potential difference (V)
I = r
...
s
...
m
...
Current (A)
R = Resistance (Ω)

\ =
𝑃

𝑉0
𝑅

] = Mean power dissipated in a resistor (W)
𝑃
V = r
...
s
...
c
...
c
...


A d
...
current makes the dot on the monitor move to the
top/bottom of the screen
...
c
...


PH5 Notes

Radioactivity and Isotopes
There are 3 types of nuclear radiation
...


This diagram shows the
penetration strengths of
each type of radiation
...

You could also use a cloud
chamber to distinguish
between radiation types
...

Sources for background radiation:
- Radon gas
- Cosmic rays

PH5 Notes

𝑁 = 𝑁' 𝑒 -_7
N = Number of radioactive nuclei
N0 = Initial number of radioactive nuclei
λ = Decay constant (s-1)
t = Time (s)

𝑁 =

𝑁'
2`

N = Number of radioactive nuclei
N0 = Initial number of radioactive nuclei
x = Number of half lives passed

𝐴 = 𝐴' 𝑒 -_7
A = Activity (Bq)
A0 = Initial activity (Bq)
λ = Decay constant (s-1)
t = Time (s)

𝐴 =

𝐴'
2`

A = Activity (Bq)
A0 = Initial activity (Bq)
x = Number of half lives passed

Uses of Radioisotopes
- You can use a gamma emitter (e
...
Cobalt-60) to sterilise medical
equipment or food
...
g
...

Biological hazards of ionizing radiation
They are dangerous because of their energy
...

- α-sources inside the body are dangerous, because they cannot pass
through your outer skin, so they cause a lot of ionisation, releasing a lot
of energy into the surrounding cells
...


PH5 Notes
You must be able to derive the equation 𝜆 =

bc0
de

f

You start with the equation for activity:
𝐴 = 𝐴' 𝑒 -_7
After one half life has passes, t = T1/2 and A = 1 2A0
...

𝜆 =

f

𝑙𝑛2
𝑇
...

EXAMPLE:
Calculate the nuclear binding energy of
h
0

Mass of 𝐻𝑒 nucleus: 4
...
007276 u
Mass of a neutron: 1
...


You know that you have 2 protons and 2 neutrons
...

2 × 1
...
008665 𝑢 = 4
...

4
...
001506 𝑢 = 0
...
030376 𝑢 × 931 = 28
...

Divide the binding energy by 4 (the number of nucleons
...
28 ÷ 4 = 7
...

Heavier nuclei can undergo fission to
decrease their nucleon number, and
increase their stability
...

All of the other elements want to have their
binding energy per nucleon as high as Iron56, so they undergo either fusion or fission
to try and achieve this
...

Fusion gives out more energy per nucleon than fission because the increase
in binding energy per nucleon are much larger for fusion reactions (in the
graph above, this is shown by the gradient being more steep
...


PH5 Notes
Nuclear Reactors
Nuclear power is a common source of electricity
...


Control rods:
- They absorb neutrons to decrease the total number of neutrons
available for fission
...

- E
...
High boron steel
...

- The material must be a poor absorber, and have light nuclei, so that
kinetic energy is transferred to the moderator’s nuclei
...
g
...

- It must have a high heat capacity, and it should be a poor neutron
absorber that can’t become radioactive
...
g
...

Environmental Problems
They waste produced remains radioactive for thousands of years, so it needs
a stable and safe place to be stored
...

- Encasing it in cement inside stainless steel drums
...

If you plot the results, it’ll look something like this:

The point P is when the spring has reached its
elastic limit, and beyond this point, the spring is
permanently stretched
...

You measure the extension by
recording the distance moved by the
paper rider, whilst varying the mass of
the load
...


Area under the line = Work done = Elastic potential

...
The limit of
proportionality
...
The elastic limit
...
The yield point
...
The breaking stress
...
The breaking point
...


PH5 Notes
A Deformation in a Ductile Metal

This is an edge
dislocation
...


Edge dislocations can cause large deformations in the following way:
- Large stresses can cause a crystal plane to snap, producing two edge
dislocations, which migrate in opposite directions
...


The following things hinder the movement of dislocations, making the alloy
harder and more brittle:
- Foreign (impurity) atoms
- Grain boundaries
- Other dislocations

PH5 Notes
Superalloys
Superalloys have been developed to work in extreme conditions, e
...
gas
turbine blades
...
g
...

- Using single crystals, therefore avoiding the weakness associated with
grain boundaries
...

Metals with smaller grains are stronger because:
- They are more difficult to be fractured because there are more grain
boundaries
...

The mechanical properties of metals can be controlled by the following
processes:

-

It makes the metal stronger
...


PH5 Notes

-

The elastic limit is raised
The higher the temperature, the smaller the grains, and the harder and
more brittle the resulting metal
...

The resulting metal is softer, and more easily bent
...
g
...


Brittle Fractures

It is accelerated by the presence of surface imperfections or cracks,
decreasing the breaking stress
...


Crack

Because the stress lines are concentrated
around the crack, this magnifies the stress,
causing the crack to extend
...

Crack propagation is more difficult under
compression
...

For glass fibres, the breaking stress increases as the diameter increases
...

Prestressed glass and concrete have been designed to reduce crack
propagation
...


PH5 Notes

Why does rubber behave like this?
Because it’s a polymer it consists of long chains of repeated units
...

- Successive C-C bonds are at an angle to each other
...
g
...
) However, it can also be a nuisance (e
...
the rolling resistance of
car tyres
...
This is the introduction
of cross-linkages
...

The strands of lamellae are held together by Van der Waals forces
...

AB = A neck forms
...

C = The stronger covalent bonds
take the strain
...

Examples:
- Vehicle tyres
o Rubber reinforced with woven cords
...
)

-

Fibre reinforced polymers (e
...
glass or carbon)
o Stiff fibres of carbon/glass are embedded in a tough matrix
(background material
...

o Chipboard – Chips or fibres of wood embedded in a matrix of
glue

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