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The Charge/Mass (e/m) Ratio of the Electron
PHYS 0212: Introduction to Laboratory Physics Fall 2012

Abstract
The experiment conducted demonstrated correlation between the charge and mass of an electron and the behavior of magnetic fields. The lab was divided into four parts. The first three parts were conducted with a compass that was used to locate the magnetic field lines around a bar magnet, a solenoid and then a pair of Helmholtz coils. As a result of these trials, our observations found evidence that magnetic field lines go from a north magnetic pole to a south magnetic pole. These results were seen in all three magnetic devices. When determining the magnitude of the electric field in the Helmholtz coils, the α value was experimentally determined to be 8.522×10-4 T/A and this value differed by 9.378% from the expected α value of 7.791×10-4 T/A. Lastly, in the fourth part of the experiment, the charge to mass ratio was calculated by bending an electron beam in side an e/m tube with the Helmholtz coils and came out to be 1.158×1011 C/kg, with a 34.17% error from the expected value 1.759×1011 C/kg.

Introduction and Theory
The easiest way to describe magnetic forces is by recognizing that unlike poles attract each other while like poles repel. Kind of like the same way an electrical positive charge is attracted to an electrical negative charge. The main difference between an electrical force and a magnetic force is while positive and negative charges have the ability to be separated, it is not possible to separate opposite poles of a magnet to create what is theoretically known as a magnetic monopole. In fact, if a magnet were cut, it would create two new magnets both with a north and south pole. This phenomenon would be observed in each piece because a north and south pole must always exist opposite each other. Electric and magnetic fields are very similar because both can create electromagnetic waves. Each wave is perpendicular to the other, and are also perpendicular to the direction they travel. Magnetic fields can be displayed by bar magnets, solenoids, and Helmholtz coils. In this lab will examine each of these objects and devices to determine how each relates to and affects a magnetic field.

Part I – The Bar Magnet
As a general rule, when drawing electric field lines, they are shown originating from a positive charge and ending on a negative charge. Similarly, as shown in Figure 9.1 on the next page, magnetic field lines can be shown originating on the north pole of the magnet and then travel back toward the south pole. The difference between electric and magnetic fields is that this motion of the magnetic field lines does not end at the south pole. Instead, the magnetic field lines create a loop by flowing through the bar and returning to the north pole. Field orientation is always determined by the north and south pole because the field lines always travel from north pole to the south pole in a continuous loop. And similarly to electric field lines, the closer the

field lines are to one another, the stronger the magnitude of the electric field. Meaning that the magnetic field of a bar magnet is strongest inside the bar and at the ends with the poles.

Figure 9.1 Part II – The Solenoid
Another type of magnet, where an electric current I flows through a conducting object, inducing a magnetic field, is called an electromagnet. When there is no current (no moving charges within the object), there is no magnetic field. While an electromagnet is functioning, the magnetic field depends upon the current and the direction of its flow. A north-south dipole is created when electrons travel in one direction through a wire, but then an opposite dipole is formed when the electrons flow in the reverse direction. The orientation of the magnetic field lines form closed loops in the wires of electromagnets just as they did with the bar magnet. Field direction depends on the direction of current flow and can be...
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