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1 Chapter 1: The "Motor effect" by australiancurriculumphysics - Friday, December 12, Overview of Electromagnetism Electromagnetism is one of the four fundamental forces that exist in our universe. There are four fundamental equations of electromagnetism, known as `Maxwell s equations which describe how charges produce electric and magnetic fields. There are also two `force laws which describe how electric and magnetic fields exert forces on charges. A descriptive summary of Electromagnetism The following is a short, snappy summary of electromagnetism. 1. Charges produce electric fields & electric fields exert forces on charges 2. Moving charges produce magnetic fields & magnetic fields exert forces on moving charges 3. A changing (time varying) magnetic field produces an electric field & a changing electric field produces a magnetic field. Isn t electromagnetism beautiful in its symmetry? A more sophisticated qualitative description of Electromagnetism We can tease the very short summary in the previous section out a little into two parts, firstly, how electric charges produce electric and magnetic fields, and secondly, how electric and magnetic fields exert forces on charges. How electric charges produce electric and magnetic fields The table below contains a little more detail about the type of electric and magnetic fields that be generated by electric charges. The four statements in this table are designed to have a one-to-one correspondence with Maxwell s four equations of electromagnetism. 1 / 5

2 each of Maxwell s equations. Qualitative description of Just for fun, here are Maxwell s equations in integral form, along with an engraving of Maxwell himself. James Clerk Maxwell by G. J. Stodart, (Right) Maxwell s equations. (Left) Engraving of The forces on a charge due to electric and magnetic fields We have covered (briefly and qualitatively) how charges produce electric and magnetic fields. In this section we will deal with how electric and magnetic fields exert forces on charges. The force on a charge due to an electric field In the preliminary course you should have been introduced to the equation relating the electric field 2 / 5

3 strength to the force on a charge We will use this equation in the first part of the topic Ideas to Implementation. The force on a moving charge in a magnetic field Experimentally, the force on a charge moving with a velocity at an angle to a magnetic field is found to be: (1) in a direction given by the right-hand-rule shown below. The right hand rule specifies that the force on a positive charge moving in a magnetic field is in the direction of the palm of your right hand, if your thumb points in the direction of the velocity of the charge and your fingers in the direction of the magnetic field. The force on a negative charge is in the opposite direction. The right hand palm rule. This means that in a reference frame in which the charge is stationary, there is no magnetic force on the charge. If the charge is moving, but it is moving along the field lines, so that or, then there is no magnetic force. We will use this equation in the first part of the topic Ideas to Implementation. The force on a current carrying wire in a magnetic field In the current topic, Motors & Generators, we are interested in applying the fundamental equation for the force on a charge moving in a magnetic field, equation (1) to determine the force on a length of wire carrying a current (which consists of moving charges) in a magnetic field. 3 / 5

4 If the charges that are moving through a magnetic field are part of a current in a conductor, then we can determine the force that acts on the conductor as a whole by adding up the forces on each individual charge which makes the current. If is the density of free electrons in the conductor, then the number of current carrying charges in a volume (where is the area of the segment of wire and its length) is. Each of these electrons carries charge and travels with a drift velocity. Using equation (1), the total force acting upon the conductor is therefore We note that the current through a conductor of cross-sectional area The force is therefore is given by (2) in a direction that can also be obtained from the right hand rule in figure where in this case the velocity of the charges is the direction of current flow in the wire, as illustrated below. carrying wire with length L in a magnetic field that is directed into the page. The force on a current top Cite this chapter as: T.E. Humphrey, Chapter 1: The Motor effect, in Fathoming Physics (HSC), December 12, 2014, 4 / 5

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