AH 3.1.7 Particles from Space Flashcards
Look at the diagram below then answer the questions
a) What type of charge is carried by the particle whose motion is shown?
b) What is the shape of the curved path?
c) Explain why the particle moves in the way.
d) State the equation for the Lorentz Force felt by the particle
e) What mnemonic helps you remember the direction of the Lorentz Force?
a) Negative
b) Parabolic
c) The particle has two components of motion
1 - a uniform velocity to the right of the page
2 - a uniform acceleration caused by the Lorentz Force acting to the
bottom of the page
d) F = qvB
where F = Lorentz Force (N)
q = charge of particle (C)
v = velocity of particle (ms-1)
B = magnetic field strength (Tesla)
e) The Right Hand Motor Rule (for electric current)
An electron moves with a speed of 4.8 × 106 m s–1 at right angles to a uniform magnetic field of magnetic induction 650 mT.
Calculate the magnitude of the force acting on the electron.
F = qvB
F = 4.99 × 10–13 N
A proton moves in a circular orbit of radius 22 mm in a uniform magnetic field of induction 920 mT, as shown in the diagram below.
a) Why does the proton move in a circle?
b) Calculate the speed of the proton.
a) The Lorentz Force qvB = mv2/r = the centripetal force required for the uniform circular motion at this particular radius
b)
qvB = mv2/r
v = 1.94 × 106 ms-1
Explain the helical motion of charged particles in a magnetic field B using the equation F=BqV
This particle has two velocity components:
- the tangential velocity of its uniform circular motion - this is, as all times, perpendicular to the magnetic field according to F=qvB using the Right-hand Motor rule. On its own this is simply uniform circular motion.
- A smaller velocity component parallel to the Magnetic filed direction On its own this would produce linear motion.
When these two component occur together for a particle they combine to produce a resultant velocity which follows a helical path, as shown below.
Describe the origin and composition of cosmic rays
Origin
Cosmic Rays are high energy particles travelling at near-light speeds which reach the Earth and which have originated elsewhere. They originate in the Sun but also from elsewhere in our galaxy and form beyond our galaxy.
Composition
Cosmic rays come in a whole variety of types, but the most common are protons, followed by Helium nuclei (alpha particles). There is also a range of other nuclei as well as individual electrons and gamma radiation. See the table below.
Compare the energies and types of cosmic rays with particles produced in particle accelerators on Earth
The energies of cosmic rays cover an enormous range, with the most energetic having energies much greater than those capable of being produced in current particle accelerators on Earth.
The highest energies produced in particle accelerators on Earth are of the order of 1 TeV (Teraelectronvolt) = 1012 eV.
Cosmic rays have been observed with energies ranging from 109 to 1020 eV. Those with energies above 1018 eV are referred to as ultra-high-energy cosmic rays (UHECRs).
What happens when Cosmic Rays interact with the Earth’s atmosphere?
When cosmic rays reach the Earth, they interact with the Earth’s atmosphere, producing a chain of reactions resulting in the production of a large number of particles known as a cosmic ray shower. When cosmic rays from space (primary cosmic rays) strike particles in the atmosphere they produce secondary particles, which go on to produce more collisions and particles, resulting in a shower of particles that is detected at ground level. This is shown in the diagram below.
Describe and explain the solar cycle.
Sunspots are magnetic regions on the Sun with magnetic field strengths thousands of times stronger than the Earth’s magnetic field. They appear as black spots on the solar surface. The number and activity of sunspots peaks approximately every 11 years - this is called the solar cycle. Solar activity peaks in line with sunspot peaks. This is why aurora are more common and more intense during the peak of the solar cycle.
Describe and explain the solar wind including its composition.
The outer atmosphere of the Sun, the Corona, has a temperature of two million °C means the particles of the corona are moving very fast indeed. So fast, that the Sun’s gravity cannot hold on to them, and they stream away from the Sun in what is called the solar wind.
The solar wind is a stream of electrically charged particles that flows constantly out from the sun in all directions. It is composed of approximately equal numbers of protons and electrons (i.e. ionised hydrogen). It can be thought of as an extension of the corona itself and as such reflects its composition. The solar wind also contains about 8% alpha particles (Helium nuclei) and trace amounts of heavy ions and nuclei (C, N, O, Ne, Mg, Si, S and Fe).
The solar wind travels at speeds of between 300 and 800 kms–1, with gusts recorded as high as 1000 km–1 (2.2 million miles per hour). The particles can make the journey from the sun to the Earth in fewer than 10 days.
Describe and explain how the solar wind interacts with the Earth’s atmosphere.
When the solar wind particles encounter the Earth’s magnetic field travelling at speeds between 300 and 800 km/s, the vast majority of them are deflected around the Earth, rather like water flows around a stone in a river - see the picture below.
However, some incoming solar wind protons and electrons interact with particles in the Earth’s atmosphere causing ionisation of Nitrogen atoms and excitation of orbiting electrons in Oxygen and Nitrogen atoms.
When a Nitrogen atom regains its electron in the upper atmosphere, it emits a photon. When the promoted electron in the Oxygen or Nitrogen atom returns from its excited state back to the ground state, it emits a photon.
Oxygen emissions are typically green or orange-red depending on the energy involved.
Nitrogen emissions are blue if it regains an electron and red if caused by an electron returning to the ground state.
Some particles travel down along the Earth’s magnetic field lines, gain additional energy and lose it to the atmosphere in the auroral zone producing the characteristic coloured glow called the Aurora Borealis.
Describe and explain solar flares
The sun periodically releases sudden bursts of energy of up to 6 × 1025 J, an event called a solar flare. The flare ejects clouds of electrons, ions, and atoms through the corona of the sun into space. These clouds typically reach Earth a day or two after the event. Solar flares are often followed by a colossal coronal mass ejection, a huge burst of plasma and magnetic field released from the corona and forming part of the solar wind. The picture below shows a solar flare.
What effect does a magnetic field have on a stationary charged particle within the field?
None.
What effect does a magnetic field have on a moving charged particle within the field?
The moving charged particle feels a Lorentz force F.
Look the the diagram below of an electron moving through a magnetic field of induction B.
Copy the diagram and
a) add the Lorentz force acting on the electron
b) State the equation for the force on the electron
c) What difference would there be if the electron were eplaced by a positron (same mass, opposite charge)?
a) see diagram below
b) F = B q v sinθ
c) The force woould be directed in the opposite direction (downwards).
Copy this diagram and add the force felt by the electron as it enters the magnetic field. Indicate the angle between the electron’s direction of motion and the directions of the force and magnetic induction. State the equation which gives this force.
As the diagram shows, the resulting Lorentz Force is at right angles to the electron’s velocity and at right angles to the magentic induction.
F = Bqv
a) Copy this diagram and add the resulting Lorentz Force, F.
b) What is the angle between the Lorentz Force and the electron’s velocity?
c) In such circumstances, what motion will the electron exhibit? Why?
d) Establish a force equation equation and so derive an expression for the radius r.
a) See below.
b) 90o
c) Uniform circular motion, beacause there is an umbalanced force acting on a body at right angles to it’s uniform velocity vector.
d) Uniform circular motion means there must be a centripetal force Fc = mv2/r
The casue of this centripeal force is the Lorenzt force FL = B q v = B e v …as the charge is an electron.
So mv2/r = B e v
r = mv2 / B e v
r = mv/B e
Copy and complete this diagram to show the path of an alpha, beta and gamma as they pass through a magentic field from the bottom of the page and leave it at the top. Assume that the alpha and beta particles anter at the same speed,
Suggest why we do not see complete circular motion exhibted by alpha, beta or gamma here.
See the diagram below.
Gamma has no charge so feels no Lorentz force under any circumstances so is always undeviated. Circular motion is therefore impossoble for gamma here. The gamma ray simply passes starigth through the field undeviated.
Alpha and beta each begin to describe circular motion but the radius of each motion is so large that they do not have time to complete a circle before exiting the magnetic field at the top.
Note that alpha, being MUCH heavier than beta, deflects less i.e. has a much larger radius of curvature.
The diagram below shows a particle P describing uniform circular motion in a clockwise direction.
Copy the diagram and indentify clearly
- the magnetic induction B and it’s direction
- the instantaneous velocity v of the particle
- the direction of the Lorentz force F
- the charge on the particle
See below for the completed diagram.
The particle must be positive to be travelling in the circle show - this is found using the Right Hand Motor Rule for ELECTRONS then reversing the force direction to match the required centripetal force direction here.
