So, according to classical theory, electrical and gravitational forces are absolutely separate and distinct phenomena.

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1 Chapter 21 Magnetic Forces and Magnetic Fields Thursday, March 11, :26 PM According to classical theory, there is no connection between electric charge and gravitational forces. Gravitational forces act on particles that have mass; if these same particles also have electric charge, the electric charge has no influence whatsoever on the gravitational forces acting. Similarly, the source of a gravitational field is mass; electric charge does not (according to classical theory) have any influence on creating any gravitational field. So, according to classical theory, electrical and gravitational forces are absolutely separate and distinct phenomena. As scientists learned about various interactions in nature, including gravitational, electrical, magnetic, nuclear, and so on, and progress was steadily made in understanding them, occasionally it was found that two interactions that were previously thought to be separate and distinct were eventually found to be intimately related. This is always a big deal in science, and is a sign that our understanding has taken a big step forward. Electric and magnetic phenomena were once thought to be separate and distinct, but the discoveries of Oersted, Faraday, and others in the 1800s made it clear that there was a deep connection between electric and magnetic phenomena. Maxwell's equations, in the 1860s, his subsequent prediction of electromagnetic waves, and Hertz's experimental confirmation of electromagnetic waves in 1887 were important milestones in the history of the unification of electric and magnetic phenomena. In this chapter, and the next two, we'll learn about magnetism and we'll learn more about the intimate connections between electric and magnetic phenomena. We'll start by recalling some basic facts about magnets and Ch21L Page 1

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7 Now continue to determine the net magnetic field at positions 2 and 3 in the same way. Example: The two insulated wires in the figure cross at a 30 angle but do not make electrical contact. Each wire carries a 5.0 A current. Points 1 and 2 are each 4.0 cm from the intersection and are equally distant from both wires. Determine the magnitudes and directions of the magnetic fields at points 1 and 2. Ch21L Page 7

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10 Observe that the force vector is perpendicular to both the velocity vector and the magnetic field vector. Another way to say this is that the force vector is perpendicular to the plane defined by the velocity and magnetic field vectors. Ch21L Page 10

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15 Example: Determine the torque on a square current loop with sides of length 5 cm and carrying a current of 0.5 A if the axis of the loop is inclined at an angle of 30 degrees relative to a uniform magnetic field of magnitude 1.2 T. Solution: Ch21L Page 15

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17 Problem: Consider two particles that orbit the earth's magnetic field lines. Calculate the frequency of the circular orbit for (a) an electron with speed m/s, and (b) a proton with speed m/s. (The strength of the earth's magnetic field is approximately T.) Solution: Ch21L Page 17

18 Problem: A mass spectrometer similar to the one in the figure is designed to separate protein fragments. The fragments are ionized by the removal of a single electron, then they enter a 0.80 T uniform magnetic field at a speed of m/s. If a fragment has a mass that is 85 times the mass of the proton, determine the distance between the points where the ion enters and exits the magnetic field. Problem: The two 10-cm-long parallel wires in the figure are separated by 5.0 mm. For what value of the resistor R will the force between the two wires be N? Ch21L Page 18

19 Problem: An electron travels with a speed of m/s between two parallel charged plates, as shown in the figure. The plates are separated by 1.0 cm and are charged by a 200 V battery. What magnetic field strength and direction will allow the electron to pass between the plates without being deflected? Ch21L Page 19

20 The previous problem suggests an idea for a velocity selector. By adjusting the magnetic field strength (and direction) appropriately you can ensure that only particles with a chosen velocity can make it through the apparatus in a straight line. By placing some absorbing material at the right end of the apparatus, with a small opening, you can ensure that particles of a certain velocity are selected by the apparatus. This is important, for example, for mass spectrometers, that require particles of given velocity for their operations. Problem: A 1.0-m-long, 1.0-mm-diameter copper wire carries a current of 50.0 A towards the East. Suppose we create a magnetic field that produces an upward force on the wire exactly equal in magnitude to the wire's weight, causing the wire to "levitate." What are the magnetic field's magnitude and direction? Ch21L Page 20

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