The Movement of Charged Particles in a Magnetic Field

1. The Movement ofCharged Particlesin aMagnetic Field By Emily Nash And Harrison Gray

2. Preview • Magnetic fields and how they are created • Magnetic field of the earth • Solar wind and how the earth’s magnetic field affects it • Taking a look at the force that magnetic fields exert upon electrons by using a cathode ray tube, magnets, and some simple math.

3. Magnetic Fields Magnetic Fields are created by moving charged particles, and only affect moving charged particles. Forces between two electric currents is what causes a magnetic force. Two parallel currents flowing in the same direction attract each other, while two parallel currents flowing in opposite directions repel each other. N When there exists a steady stream of electrons, a negatively charged particle, an electric current forms, which produces a magnetic field. This force leads to the idea of the north and south poles of a magnetic field. S

4. Creating a Magnetic Field It is possible to create a magnetic field by producing an electric current, or vice versa. When current passes through a coil of wire, it generates a magnetic field along the access of the coil. This is called electromagnetism current

5. Earth's Magnetic Field The Earth itself is a magnet, with a magnetic north pole and south pole. The origin of the Earth’s magnetic field is said to be a result of the dynamo effect, electric currents produced by the rotation of the iron-nickel core. S N The Earth’s magnetic field continually traps moving charged particles coming from the sun, called solar wind. High concentrations of these particles within the field are called the Van Allen Radiation belts.

6. Solar Wind Magnetotail Solar Wind consists of gases comprised of protons, electrons, and ions which hurl towards the earth from the sun at velocities of 450 km/sec or higher. Bow Shock Magnetosheath The path of these particles change almost directly as they hit the earth’s magnetosphere at the region called the bow shock. The impact of the solar wind causes The field lines facing the sun to compress, While the field lines on the other side stream back to form a Magnetotail. Because the charged particles of the rays are deflected around the magnetosheath, the earth is protected from most of the deadly radiation.

7. Solar Wind Cntd Some solar wind particles, however, do escape the earth’s magnetosphere and contribute to the Van Allen radiation belts. • When these particles do enter the magnetic field, they go through three motions: • Spiral- the particle takes a spiraling motion around a magnetic field line. • Bounce- the particles eventually bounce towards the opposite pole, where they spiral again. • Drift- as the particle continually spirals and bounces, it drift around the magnetic field and is trapped in the magnetosphere. In order to better understand the motion of particles through a magnetic field, we have conducted an experiment involving creating an electron beam and running it through magnets as a parallel to solar wind entering the earth’s magnetic field.

8. √ Cathode Ray Tube Cntd. Since change in energy is the voltage times the charge then ½mv²=qV Therefore v= √(2qV/m) The potential energy of electrons is converted to kinetic energy Electrons are attracted to positively charged plate. They accelerate towards it and small percentage escape the plate through small hole, creating electron beam. 120 Volts Plate is heated and electrons boil off. Velocity= 0 Potential Energy= ½ mv^2 6.3 Volts

9. Cathode Ray Tube

10. Calculating the Velocity of the Electrons We now know that v= √(2qV/m), so we can now easily find the velocity of our beam of electrons. q(charge) of an electron= -1.6•10^-19 V(volts)=120 m(mass) of an electron=9.11•10^-31 kg Therefore: v=√(2)(-1.6•10^-19)(120)/(9.11•10^-31) v=√4.215•10^13 v=649•10^6 m/s

11. Bending Electron Beams In order to predict the angle at which the electrons are deflected, we must first measure the force that the magnetic field inserts upon the beam To do this, we use the equation: F=qvB Like Solar Wind, the electrons in the CRT beam are deflected when entering a magnetic field, therefore the electron beam “bends.” Magnetic field The force is always Perpendicular to the magnetic field And the velocity of the electrons Electrons

12. Calculating the Strength of the Magnetic Field In order to find the force of the magnetic field, we must first calculate its strenghth. Since F=qvB and, according to Newton’s second law, F=m•v²/r, we can deduce that qvB=m•v²/r Or B=mv/qr mass= 9.11•10^-31 kg velocity= 6.492•10^6 m/s Charge= 1.6•10^-19 C And we measured the distance of the electron beam from the magnets to be .075 meters Therefore B= (9.11•10^-31)(6.492•10^6)/(1.6•10^-19)(.075) B=2.772•10^-6 tesla

13. Calculating the Force of the Magnetic Field Now that we know the strength of the magnetic field at the electron beam, we can Calculate the force which the field exerts upon the electrons. F=qvB F=(649•10^6)/(1.6•10^-19)(2.772•10^-6 F=2.879•10^-18 N

14. Conclusion • Basics of Magnetic fields and electromagnetism • The earth’s magnetic field and how it shields the earth from solar wind • The movement of charged particles such as solar wind as they enter a magnetic field • How to find the force that magnetic field exerts upon charged particles and the strength of the field itself. • How to predict the path of a charged particle through a magnetic field