The Aurora Borealis, or the Northern Lights, results when charged particles collide with nitrogen and oxygen molecules in the upper atmosphere. During periods of increased solar activity, some of the energetic charged particles that bounce back and forth along the Earth's magnetic field... ...gain sufficient energy to rain down on the upper atmosphere and produce auroras. Auroras occur at both poles of the Earth and are usually observed at latitudes between 65 degrees and 75 degrees. In the Southern hemisphere the phenomenon is called the Aurora Australis. Before examining forces exerted on moving charged particles in the presence of a magnetic field, let's briefly review the properties of magnetic fields. Sources of magnetic fields are magnetic substances and electric currents. One of the simplest magnets is the bar magnet. It has a north and a south pole. Magnetic poles are like electric charges: they exert forces on each other. Like poles repel each other, and unlike poles attract each other. Since the Earth has an intrinsic magnetic field, when a bar magnet is free to rotate around an axis, one of its poles points toward the Earth's north pole. This is how the north pole of a magnet is defined. Since unlike poles attract each other, the north pole of a bar magnet points towards the South pole of the Earth's magnetic field. In fact, the North pole of the Earth's magnetic field is located at the Earth's South Pole! Every magnet, regardless of its shape has two magnetic poles. When a magnet is broken, each piece will have its own south and north poles. A single pole magnet -or a magnetic monopole-has never been observed. Like an electric field, a magnetic field is defined by its direction and its magnitude or strength. This picture shows the magnetic field created by a bar magnet. The traced out magnetic field lines indicate the orientation of the magnetic field. The magnetic field is tangent to any point on the line. Arrows indicate the direction that the north pole of a compass needle would point. The SI unit of the magnetic field is the weber per square meter, also called the tesla. Let's consider three particles: one stationary with respect to the magnet, one moving along the magnetic field lines, and the last one moving across the magnetic field lines. One of these charged particles will interact with the magnetic field and be given a push by the field. ... It is interesting that a force is exerted on the charged particle by the magnetic field only when the particle moves across the field lines. In other words, when a charged particle moves parallel to the magnetic field, the force exerted by the magnetic field on the charged particle is zero. How does the speed of the particle affect the force? If the particle moves faster across the field lines, will the force be Consider two more factors: the magnitude of the charge and the strength of the magnetic field. Which combination of charge and field strength creates the greatest force? Let's summarize the conclusions we've reached thus far: A charged particle must move across strong magnetic field lines at a high velocity to create a strong force. In this picture, the force vector is perpendicular to the motion of the particle. The dots represent the magnetic field lines coming out of the screen. These observations can be summarized by the formula: Force equals charge, q, times velocity, v, times the strength of the magnetic, B. This formula is true only when the motion of the particle is perpendicular to the magnetic field lines. This formula represents the maximum force resulting from a moving charge interacting with a magnetic field. What is the force on a 6 micro-Coulomb charged particle moving at 4 times ten to the 4th meters per second perpendicular to a 2.55 Tesla magnetic field? But what if the direction of the particle's velocity is not perpendicular to the magnetic field lines? In that case, we must find the component of the velocity that is perpendicular to the magnetic field. This component results in a factor of sine theta in the equation, because v sine theta is the component of the velocity that is at right angles to the magnetic field. The formula thus becomes: F = q v B sine theta. Another way of representing this is Force equals charge times the cross product of velocity with the magnetic field strength, or F equals q v cross B. The cross indicates that the cross product of two vectors is taken. A 2 times 10 to the negative 4th gram particle with a charge of 2 Coulombs enters a 4 Tesla magnetic field at an angle of 30.0 degrees ... ...and a velocityof 5 times ten to the 4th meters per second. What is the force on the particle?

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