Magnetic Fields and Electromagnetic Induction

Magnetic Fields

A magnetic field is a region where a magnetic force is experienced.

The two types of magnet are permanent magnets and electromagnets.

Permanent magnets are common and are made of iron, cobalt or nickel alloys.

Lines are drawn to represent magnetic fields. These lines are called lines of flux.

The arrows show the direction of the force.

Field direction always goes from north to south.

The spacing between the lines of flux tells you about the strength of the field. The closer together the lines, the 

stronger the field becomes (close to the poles).

Like poles repel, unlike poles attract.

Field lines never intersect.

Fleming’s left hand rule is used on electric motors and particles.

Magnetic flux density is defined as the force acting per unit current in a wire of unit length, which is perpendicular to the field.

The direction of the current is opposite to the direction of the electron.

If the magnetic field is not uniform, then the particles will move in a spiral.

A commutator can be used to prevent wires from twisting for a current in a loop. This allows the coil to keep 

rotating in one direction.

A cyclotron is a particle accelerator which uses a high frequency, alternating potential difference.

The 2 ways of varying magnetic flux density are the current (B is proportional to I) and the spacing of the coils (B is proportional to N / L)

Electromagnetic Induction

The motor effect is where the interaction of two fields (magnetic and electric) to produce motion.

Two methods of producing electricity are moving a magnet in and out of a solenoid (the dynamo (movement) 

effect) and transformers.

The dynamo converts mechanical energy into electrical energy. Electricity is passed along wires. The motor 

reverses the process and converts electrical energy into mechanical energy.

Fleming’s right hand rule is used on generators.

Faraday’s law states that the induced E.M.F is proportional to the rate of change of flux linkage.

Lenz’s law states that the induced current is always in such a direction as to oppose the motion or change causing it.

Step-up transformers have more turns in the secondary coil than the primary coil therefore the potential 

difference in the secondary coil will be greater than the potential difference in the primary coil.

Step-down transformers have less turns in the secondary coil than the primary coil therefore the potential difference in the secondary coil will be less than the potential difference in the primary coil.

Transformer rule is the ratio of the secondary potential difference to the primary potential difference is equal to the ratio of the number of secondary turns to the number of primary turns.

Transformer inefficiency is due to:

• Resistance heating in the current in each coil (this can be resolved by adding low-resistance windings).
• Induced currents which are caused by the heating effect of the eddy currents in the core (this can be resolved by adding a laminated core which consists of layers of iron separated by layers of insulator.
• Repeated magnetisation and demagnetisation of the core (this can resolved by adding a soft iron core so that it can be easily magnetised and demagnetised.

©2011 Grant Dwyer

Electric Fields and Capacitance

Electric Fields

Conductors have free electrons.

Insulators don’t have free electrons as they are attached to the atoms.

Like charges repel, unlike charges attract.

Equipotentials are lines of equal potential.

Equipotential surfaces are perpendicular to field lines.

Any electrical conductor is an equipotential surface.

Coulomb’ law states that any 2 charged particles exert a force on each other which is proportional to their 

charges and inversely proportional to the square of their distance apart.

Air is an insulator but during a thunderstorm, the insulating properties break down due to the electric field 

between the clouds and the ground.

ε₀ is the measure of how well a medium will permit an electric field to pass through it.

Electrical potential is the work done per unit charge on a small positively charged object to move it from 

infinity to that point in the field.

Electric fields can be attractive and repulsive, gravitational fields are only attractive. Both fields can be 

represented by inverse square laws.

Electric field strength at a certain point in an electric field is defined as the force per unit charge on a positive test charge placed at that point.

Electric field is equal to the negative of the potential gradient.

No work is done when a charged particle moves along a line of constant potential.

Electric potential is a scalar quantity.

Electric field strength is a vector quantity.

Potential gradient is a point in a field where the change in potential per unit change of distance along the field 

line at that point.       

Capacitance

Capacitors store electrical energy.

Charge a capacitor by connecting it to a battery.

Discharge a capacitor by disconnecting from the battery and attaching it to the circuit.

The time taken to charge or discharge depends on the capacitance (which affects the charge) and the 

resistance (which affects the current).

Dielectric is an electrical insulator which can be a solid (ceramic, mica, glass, plastics and oxides of various metals), liquid (distilled water), gas (dry air) or a vacuum.

©2011 Grant Dwyer

Simple Harmonic Motion and Gravitation

Simple Harmonic Motion

Description of a bob - Starting from the equilibrium position, it moves in one direction, back to equilibrium and moves in the other direction, and back to equilibrium again.

At centre - displacement = 0 , velocity = max , acceleration = 0

At the maximum displacement - displacement = amplitude , velocity = 0 , acceleration = max

SHM - the acceleration is proportional to the displacement from a fixed point and is directed towards that fixed point.

ω is the constant of proportionality.

The negative sign is directed towards the fixed point.

Damping is the process whereby energy is taken from the vibrating system to minimise the effect of resonance.

Under and heavy damping quickly reduces the amplitude to zero.

Critical damping reduces the amplitude in the shortest possible time.

Over damping takes longer for the amplitude to reach zero than critical damping.

Displacement is the distance in a given direction.

Amplitude is the maximum displacement from equilibrium of an oscillating object.

Period is the time for 1 oscillation.

Frequency of an oscillating object is the number of cycles of oscillations per second.

Phase difference is measured in radians, for 2 objects oscillating with the same time period (T), where phase 

difference is 2 π t / T

Resonance is the amplitude of vibration of an oscillating system which is subjected to a periodic force which is 

largest when the periodic force has the same frequency as the resonant frequency of the system.

Periodic force is a force that varies regularly in magnitude with a definite time period.

Resonant frequency is the frequency of an oscillating system in resonance.

Gravitation

Gravitational fields are only attractive.

Gravitational field strength is the point in a body’s field as the force is exerted on an object placed at that point 

per kilogram of the objects mass.

GPE is the energy of an object due to its position in the gravitational field.

GPE is zero at infinity as the object is so far away that the effect of gravity is negligible.

GPE is negative on the surface of the Earth as an object needs energy to overcome the gravitational field.

GPE is the work done to move a small object from infinity to that point.

Gravitational potential at a point in a gravitational field is the work done per unit mass to move a small object 

from infinity to that point.

Radial Field is where field lines are straight and converge as if from a single point over a large distance.

Uniform field is a region where the field strength is the same in magnitude and direction at every point in the field over a small distance.

The potential gradient at a point in a gravitational field is the change in potential per metre at that point.

Equipotentials are lines of equal potential.

Equipotential surfaces are perpendicular to field lines.

Kepler’s law states that T² is proportional to r³.

Geostationary satellites stay over the equator with a circular orbit which takes 24 hours to fully orbit the Earth in the same direction.

Geosynchronous satellites repeatedly orbit regular points over the Earth over time.

Newton’s law of gravitation states the gravitational force between two point masses at distance apart is given by F = G m M / r².

©2011 Grant Dwyer

Momentum and Circular Motion

Momentum

Newton’s first law states that an object stays at rest unless acted on by an external force.

Newton’s second law states that force is proportional to the rate of change of momentum, unless acted on by an external force.

Newton’s third law states that an action has an equal and opposite reaction.

The Principle of Conservation of Momentum - In a collision, the momentum before the collision is equal to the momentum after the collision, unless acted on by an external force.

The Principle of Conservation of Energy – The total energy after the change is always equal to the total energy before the change, unless acted by an external force.

Area under force-time graph is impulse/momentum.

An elastic collision is where kinetic energy is conserved, but most collisions are inelastic.

Linear momentum is the momentum in a straight line (p = mv).

Circular Motion

In circular motion, linear velocity is at tangents around a circle at any point.

Acceleration and force are directed towards the centre of the circle.

Angular velocity is the velocity around the circle.

An object changing velocity around the circle means that it is accelerating with a constant speed. This is because the direction is constantly changing.

Centripetal force and acceleration are towards the centre of the circle.

Centrifugal force is away from the centre of the circle.

1 radian is equal to 57.3 degrees.

©2011 Grant Dwyer

Nuclear Reactor

The neutrons that are produced in the reaction can then go on and be part of other reactions, creating a chain reaction.

The neutrons that are used are low energy (thermal neutrons) as they can only be captured in this way.

The amount of fissionable material necessary for the chain reaction to sustain itself is called the critical mass.

The moderator slows down or/and absorbs neutrons.

The moderator needs to be able to slow down some neutrons enough to cause further fission and that absorbs more neutrons the higher the temperature will decrease the chance of meltdown.

Water can be used as a moderator.

The control rods control the chain reaction by limiting the number of neutrons in the reactor. These absorb neutrons so that the rate of fission is controlled. Boron can be used as control rods.

Control rods can be inserted by varying amounts to control the reaction rate but in an emergency the reactor will be shut down automatically by the release of the control rods into the reactor.

Boron can be used as control rods.

Coolant is sent around the reactor to remove heat produced in the fission.

Water can also be used as a coolant.

The heat from the reactor can then be used to make steam for powering electricity-generating turbines.

When a neutron is released, one or more of the following events can occur:

• slowed down by the moderator
• taking about 50 collisions to reach thermal speeds
• absorbed by uranium-235 to cause fission event
• one neutron released goes on to cause a further fission is the critical condition
• a neutron may leave the reactor core without further interaction
• be absorbed by uranium-238
• be absorbed by a control rod
• be scattered by uranium-238
• be scattered by uranium-235

The reactor core is thick steel to withstand high temperature and pressure.

The core is within thick concrete walls which absorb neutrons and gamma radiation.

High level waste– spent fuel rods are stored in cooling ponds for at least a year. They are also stored in sealed containers underground.

Intermediate level waste – stored in sealed drums and then encased in concrete, then stored in specially constructed buildings with walls of reinforced concrete.

Low level waste – sealed in metal drums and stored in trenches.

©2011 Grant Dwyer

Properties of Radiation

Properties	Alpha Radiation (α)	Beta Radiation (β)	Gamma Radiation (γ)
Nature	2 Protons and Neutrons	β+ = Electron β- = Positron	Photon of Energy of the Order of MeV
Range in Air	Fixed Range (Depends on Energy which can be up to 100mm	Range up to about 1m	Follows the Inverse Square Law (See Equations)
Deflection in a Magnetic Field	Easily Deflected	Opposite Direction to α particles and more easily deflected	Not Deflected
Absorption	Stopped by Paper or Thin Metal Foil	Stopped by Approximately 5mm of Aluminium	Stopped by Several Centimetres of Lead
Ionisation	Produces about 104 Ions per mm in Air at Standard Pressure	Produces about 100 Ions per mm in Air at Standard Pressure	Very Weak Ionising Effect
Energy of Each Particle/Photon	Constant for a given Source	Varies up to a Maximum for a given Source	Constant for a given Source
Danger Inside and Outside of the Body	Inside: Dangerous Outside: Less Dangerous than β and γ	Inside: Less Dangerous than α Outside: Dangerous	Inside: Less Dangerous than α Outside: Dangerous

©2011 Grant Dwyer

Kinetic Theory

The assumptions for an ideal gas for kinetic theory are:

• the gas contains a large number of particles
• the particles move rapidly and randomly
• the motion of the particles follows Newton’s laws
• collisions between particles themselves or at the walls of a container are perfectly elastic
• there are no attractive forces between particles
• any forces that act during collisions are instantaneous
• particles have a negligible volume compared with the volume of the container

A particle moves with speed, c, in a square box of length L

The components of c in three dimensions are u, v and w.

You can show that c² = u² + v² + w² - An extension of pythagoras in 3 dimensions.

Particle of mass, m, and velocity, u₁.

Momentum = m u₁

Change in momentum = -2m u₁

F = change in momentum / time = -2m u₁ / t

u₁ = 2L / t

t = 2L / u₁

F = -m u₁² / L

P = F / A = (m u₁² / L) / A = m u₁² / V

Total Pressure = (m / V) (u₁² + …...+ u_N²) = m N u² / V

u² is only in one direction so c is in 3 direction which gives u² + v² + w²

c_rms² = u_rms^{2 +} v_rms^{2 +} w_rms²

u_rms² = ⅓ c_rms²

P = ⅓m N c­_rms² / V

P V = ⅓m N c­_rms²

©2011 Grant Dwyer

Dark Energy

Astronomers studying the cosmic microwave background (CMB) have found new direct evidence for dark energy, the mysterious substance that appears to be accelerating the expansion of the universe. Their findings could also help map the structure of dark matter on the universe's largest length scales. The CMB is the faint afterglow of the universe's birth in the Big Bang. About 400,000 years after its creation, the universe had cooled sufficiently to allow electrons to bind to atomic nuclei. This "recombination" set the CMB radiation free from the dense fog of plasma that was containing it. Space telescopes such as WMAP and Planck have charted the CMB and found its presence in all parts of the sky, with a temperature of 2.7 K. Measurements also show tiny fluctuations in this temperature on the scale of one part in a million. These fluctuations follow a Gaussian distribution. 


For more information go to http://physicsworld.com/cws/article/news/46572

Picture Courtesy of European Space Agency

Some Laws of Science

Newton's Laws of Motion


First law states that the velocity of an object will stay constant unless acted on by an external force.


Second law states that the force is proportional to the rate of change of momentum.


Third law states that for every action there is a equal and opposite reaction.




Kepler's Laws of Planetary Motion


First law states that the orbit of every planet is an ellipse with the Sun at one of the two focus.


Second law states that a line joining a planet and the Sun sweeps out equal areas during equal intervals of time.


Third law states that the square of the orbital period is directly proportional to the cube of the semi-major axis of its orbit.




Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.




Euler's Laws of Motion


First law states that the linear momentum of a body is equal to the product of the mass of the body and velocity of its center of mass. Internal forces between the particles that make up a body, do not contribute to changing the total momentum of the body.


Second law states that the rate of change of angular momentum about a point is equal to the sum of the external moments about that point.




Archimede's principle states that any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.




Newton's law of cooling states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings.




Gas Laws


Boyle's law states that for a fixed amount of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional.


Charles's law states that for a fixed amount of an ideal gas kept at a constant pressure, volume and temperature are directly proportional.


Gay-Lussac's law states that for a fixed amount of an ideal gas kept at a constant volume, pressure and temperature are directly proportional.


Avogadro's law states that the volume occupied by an ideal gas is proportional to the amount of moles present in the container.




Laws of Thermodynamics


Zeroth law states that if system A and system B are in thermal equilibrium with system C, then system A is in thermal equilibrium with system B.


First law states that in a thermodynamic process, the increment in the internal energy of a system is equal to the difference between the increment of heat accumulated by the system and the increment of work done by it.


Second law states that no process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.


Third law states that the entropy of a perfect crystal approaches zero as temperature approaches absolute zero.

Airplanes Can Make it Rain

Humans can encourage rain or snow by "seeding" clouds by dispersing small particles into the atmosphere. These particles act as nuclei onto which droplets of liquid water inside clouds can freeze, producing ice crystals that, when large enough, fall to Earth in the form of snow or rain. These droplets often exist in a "supercooled" state at temperatures as low as –38 °C and the introduction of particles into clouds raises this minimum temperature. Due to this process which has been noticed in recent years, there is more precipitation around airports. 


For more information go to http://physicsworld.com/cws/article/news/46388

Picture Courtesy of Eric Zrubek and Michael Carmody