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Motion of Charged Particles 8.4 in Magnetic Fields Atoms and molecules are particles that are the building blocks of our universe. How do scientists study the nature of these small particles? The mass spectrometer shown in Figure 1 is an instrument scientists use to study atoms and molecules. Mass spec- trometers are used to define the elemental composition of a sample or molecule, to determine masses of particles, and to reveal the chemical structures of molecules. Figure 1 A scientist inserts a sample into a mass spectrometer. How does a mass spectrometer work? Imagine a billiard table with a billiard ball rolling across the table from your left to your right. If you hit the ball with a sideways force, the ball will move away from you. Now suppose a bowling ball rolls across the table in the same direction. If you apply the same sideways force on the bowling ball, it will also move away from you but not as far. The masses of the billiard ball and bowling ball determine the distance they will be deflected by the force. If you know the amount of force, the speeds of the balls, and the curve of their paths, you can calculate the mass of each ball. The less deflection there is, the heavier the ball must be. In a similar way, a mass spectrometer uses a magnetic field to deflect electrically charged particles. Atoms are converted into ions and then accelerated into a finely focused beam. Different ions are then deflected by the magnetic field by different amounts, depending on the mass of the ion and its charge. Lighter ions are deflected more than heavier ones. Ions with more positive charges are deflected more than ions with fewer positive charges. Only some ions make it all the way through the machine to the ion detector, where they are detected electrically. If you vary the magnetic field, different types of ions will reach the detector. Scientists use the mass spectrometer to identify unknown compounds, to deter- mine the structure of a compound, and to understand the isotopic makeup of molec- ular elements. The mass spectrometer has applications in the medical field, the food industry, genetics, carbon dating, forensics, and space exploration. @ CAREER UNKCharges and Uniform Circular Motion To understand how a mass spectrometer works, we first need to understand how a directional force affects the motion of an object-in this case, a charged particle. Consider the direction of a magnetic force Fy and how this force affects the motion of a charged particle. We know Fy = quB sin 0. For simplicity, we assume the mag- netic field, B, is uniform, so the magnitude and direction of B are the same every- where. Figure 2(a) shows a charged particle, +q, moving at velocity V parallel to the direction of B. In this case, the angle of between v and B is zero. The factor sin 0 in Fu - qvB sin 0 is then zero, so the magnetic force in this case is also zero. If a charged particle has a velocity parallel to B, the magnetic force on the particle is zero. Figure 2(b) shows a charged particle moving perpendicular to B. Now we have 9 = 90%, and sin # = 1. The magnitude of the magnetic force is thus Fy = qvB, and the force is perpendicular to the velocity. +qo (a) (b) Figure 2 (a) When the velocity of a charged particle is parallel to the magnetic field B, the magnetic force on the particle is zero. (b) When v makes a right angle with 8 (# = 90 ), the charged particle moves in a circle that lies in a plane perpendicular to B. Recall that when a particle experiences a force of constant magnitude perpen- dicular to its velocity, the result is circular motion, as shown in Figure 2(b). Hence, if a charged particle is moving perpendicular to a uniform magnetic field, the particle will move in a circle. This circle lies in the plane perpendicular to the field lines. The radius of the circle can be determined from Newton's second law and centrip- etal acceleration. Recall that for a particle to move in a circle of radius r, there must be a force of magnitude - directed toward the centre of the circle. Here, the force producing circular motion is the magnetic force, so we have The magnetic force is perpendicular to the velocity and sin 90" = 1, so we can insert FM = qVB: quB = Solving for r gives MV Now calculate the value of r for an electron that has a speed of 5.5 x 10 m/s moving in a magnetic field of strength 5.0 x 10"* T. Inserting these values into the equation r = MV kg and using IT = 170, we get qB (9.11 X 10 3 by) (5.5 x 10# (1.60 x 10- 2) 5.0 X 10 F = 6.3 x 10 m 398 Chapter 8 . Magnetic Fields This calculation shows that we can determine the radius of a particle's deflection if we know the mass of the particle. its velocity, its charge, and the strength of the mag- netic field through which it moves.Earth's Magnetic Field Charged particles travelling parallel to a magnetic field do not experience a magnetic force and continue moving along the field direction. Charged particles travelling perpendicular to a magnetic field experience a force that keeps them moving in a circular path. Charged particles with velocity components that are both parallel and perpendicular to a magnetic field experience a combination of these effects. The result is a spiral path that resembles the shape of a coil of wire. The particle travels with a looping motion along the direction of the field (Figure 6). B +q Figure 6 When the velocity of a charged particle has non-zero components parallel and perpendicular to the magnetic field, the particle will move along a spiral path. Charged particles entering Earth's magnetic field are deflected in this way. Since they are charged particles with a component of the velocity perpendicular to the magnetic field, they will spiral along the field lines toward the magnetic poles. This Figure 7 Earth's magnetic field deflects motion results in a concentration of charged particles at Earth's north and south charged particles from outside the magnetic poles (Figure 7). atmosphere. The particles travel in spiral Collisions between the charged particles and atoms in the atmosphere release light paths along the field lines toward the that causes the glow of the aurora borealis in the northern hemisphere and the aurora magnetic poles. australis in the southern hemisphere (Figure 8). Earth's magnetic field Figure 8 The aurora australis. The glow of the auroras occurs when charged particles spiral along Earth's magnetic field lines and collide with molecules in the atmosphere above the polar regions. At high altitudes in Earth's magnetic field are zones of highly energetic charged particles called the Van Allen radiation belts (Figure 9). James A. Van Allen, an American physicist, discovered the toroidal (doughnut-shaped) zones of intense radiation while studying data from a satellite he built in 1958. Van Allen was able to show that charged particles from cosmic rays were trapped in Earth's magnetic field. Most intense over the equator, the Van Allen belts are almost absent over Earth's poles Inner outer and consist of an inner region and an outer region. The outer Van Allen belt contains Van Allen belt Van Allen belt charged particles from the atmosphere and the Sun, mostly ions from the solar wind. Figure 9 The Van Allen belts are regions The inner Van Allen belt is a ring of highly energetic protons. The concentration of of charged particles and radiation charged particles and radiation can easily damage electronic equipment, so researchers trapped by Earth's magnetic field. program the paths and trajectories of satellites and spacecraft to avoid the belts.Field Theory We associate the term force with a physical action of one object on another. When we talk about the force of a bat against a baseball, our minds use a concept of contact between the objects, which transmits the force. To develop a more accurate concept of force, we need to talk about it in terms of fields. We know that all objects are made of atoms interacting without actually touching each other. There are spatial gaps between the atoms in a bat and a baseball, so the idea that the bat makes contact with the ball is deceptive. In reality, electromagnetic forces affect the interacting atoms in each object. How do we create an understanding of the gravitational, electric, and magnetic forces? We need a scientific model that describes different types of forces that exist at different points in space, and field theory does that. Field theory is a scientific model field theory a scientific model that that describes forces in terms of entities, called fields, that exist at every point in describes forces in terms of entities that space. The general idea of fields links different kinds of forces once thought of as exist at every point in space separate. Field theory states that if an object experiences a specific type of force over a continuous range of positions in an area, then a field exists in that area. Field theory can be applied in explaining the minute interactions of subatomic particles as well as describing motions of galaxies throughout the universe. Studying gravitational, electric, and magnetic forces has revealed differences and similarities between these forces and their respective fields. The electric and magnetic fields have a stronger effect on the motion of subatomic particles, such as protons and electrons, but the gravitational field has a stronger effect on large objects, such as planets, galaxies, and clusters of galaxies (Figure 10). Figure 10 Gravity controls the collision of two clusters of galaxies, while electricity and magnetism affect the release of radiation during the collision. (Colours have been added to the image to enhance the visual representation.) The electric and gravitational forces resemble each other in that the force on an object depends on the location of the object. The magnetic force, however, depends on a charged object's motion. The direction of electric and gravitational forces points from the object toward the charge or mass source. The direction of the magnetic force depends on the motion of charged particles with respect to the magnetic field. Despite these similarities and differences, field theory states that electric and mag- netic fields are more closely related to one another than they are to the gravitational field. In fact, the electric and magnetic fields are thought to be different aspects of a single field, the electromagnetic field. They are used in conjunction with one another in a multitude of innovative technologies ranging from particle accelerators to artificial hearts