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Transcript
16.1 Two types of charge (plus neutral) Wednesday, July 15, 2015 4:06 PM Evidence: Hang various materials that have been rubbed with other materials. Charged material A will repel other charged material A. Charged material B will repel other charged material B. Charged material A will either attract or repel, but never have no effect, on charged material B. Similarly charged material A will repel or attract charged material C. And if A attracts B then A will also attract C but only if B and C repel. Similarly, if A repels B then A also repels C but only if B and C repel. Ben Franklin chose the name positive charge to apply to a glass rod rubbed with a piece of cloth. A rubbed plastic rod will then have a negative charge (not that Franklin had any plastic to play with!) 7/15/2015 4:20 PM - Screen Clipping Ch. 16 Page 1 16.2 Modern notion of charge Wednesday, July 15, 2015 4:27 PM We now associate the positive charge with protons and negative charge with electrons. As electrons are on the outside of atoms they can be rubbed off one material and transferred to another. Ben Franklin's positively charged glass rods have had some outer electrons rubbed away. All atoms are normally electrically neutral but can temporarily have charge added or taken away. Some molecules, though electrically neutral over all, can be polar, which is to say the electrons are not evenly distributed over the molecule and one side of molecule will have a positive charge and the other side a negative charge. Water molecules are polar, and since they are found in most air, will transport charges and cause charged objects to lose their charge over time. (An electron on a negatively charged object will get attracted to the positive end of a water molecule which can move through the air and then give up that loosely held electron to any positively charged object it is attracted to.) Ch. 16 Page 2 16.3 Insulators and Conductors Wednesday, July 15, 2015 7:29 PM Some materials (metals) allow charges to be conducted through them. Such materials are called conductors. Some materials (wood, stone) do not allow charge to move through them. These materials are called insulators. There are materials intermediate to the above two categories called semi-conductors. In the modern view the difference between conductors and insulators is how firmly the orbiting electrons are attached to their nuclei. The more easily the electrons are dislodged, the better the material is as a conductor. Ch. 16 Page 3 16.4 Induced Charge; the electroscope Wednesday, July 15, 2015 7:33 PM An electroscope has two pieces of conducting foil hanging at the end of a metal rod. When a charged object, say one with a negative charge, is brought into contact with the electroscope the extra electrons that form the negative charge repel one another, sending some electrons into each leaf. Thus the leaves repel each other, and the larger the charge the greater the repelling force. This is charging by contact. When the charged object, which will still have some negative charge on it, is removed from the electroscope the charges remain on the two leaves of the electroscope and the leaves will remain separated. An electroscope (or any other conductor for that matter) can be have a charge put on the leaves without actual contact being made between the charged object and the electroscope. Bring a charged object (say negative charge) close to, but not touching, the electroscope's ball. Electrons in the ball will be repelled and move down into the two leaves causing them to repel each other. If the charged rod is now moved away the surplus electrons in the leaves will redistribute themselves over the entire electroscope returning the leaves to the original position. However, when the charged object is close to the electroscope a conducting wire can be used to connect the electroscope to the ground. The electrons being repelled by the charged object now flow along the wire to ground (which has, essentially, an infinite capacity to absorb electrons). The electroscope is now missing some of its original electrons (they are in the ground). If the wire is removed those electrons are trapped in the ground and the electroscope has a net positive charge. Some of that positive charge is distributed over each leaf so that the leaves remain separated, even when the (negatively) charged object is removed from the electroscope's vicinity. This method of putting (relatively) permanent charge on an electroscope (or other conductor) is called charging by induction. Ch. 16 Page 4 induction. Electroscopes can indicate the size of a charge because the greater the leaf separation the greater the charge. Electroscopes can also be used to determine the sign of a charge on an object if the electroscope has already been given a known charge. Suppose you put a negative charge on the electroscope. The leaves will separate. Now, if an object with unknown charge is brought near the electroscope one of two things will happen. If the unknown charge is negative that charge will repel the electrons in the ball of the electroscope, pushing them down towards the leaves, and causing the leaves to separate even further. On the other hand if the unknown charge is positive, it will attract electrons into the ball, leaving fewer on the leaves, and thus causing the leaves to lessen their separation. Answer Questions 1,3,5,8 on page 496. Ch. 16 Page 5 16.5 Coulomb's Law Thursday, July 16, 2015 7:01 PM Using a light rod suspended by a twisted fibre (like Cavendish apparatus for measuring G) Cavendish was able to determine the force equation relating the size of electric charges and the distance between them. The left hand table below shows (fictitious) data. A charge is put on one end of the suspended rod. A variable charge, of the same sign, is then brought to a set distance from the end of that rod (the variable charge is moved to keep the same set distance from the revolving rod). The rod twists until the tension in the fiber equals the repelling electric force. The right hand table shows (fictitious) data. A charge has been put on the suspended rod. A given charge is placed at various distances from the suspended rod. Once again the rod will twist until the repulsive electric force is balanced by the twisting force of the fiber. Charge Twist (deg) 1 50 1/2 27 1/4 12 1/8 7 1/16 3 Distance (cm) Twist (deg) 0.1 60 0.2 16 0.4 6.5 0.6 4 0.8 2.5 That is, the force decreases with the square of the distance and increases with the product of the charges. The equation is Coulomb's Law The value of the proportionality constant, k, is needed to make the equation useful for calculation. In modern units the value of k is 9 x 109 N-m2/C2. [A coulomb (C) is the amount of charge which, if placed on two point objects 1 m apart, will result in each object exerting a force of 9 x 109 N on the other. This is a huge force .] Note: Coulomb's Law describes the force between charges at rest. This force is called the electrostatic force or the Coulomb force. Moving charges have additional forces on them. The study of charges at rest, and forces upon them, is the area of physics called electrostatics. Note: The form of the equation is similar to the equation Ch. 16 Page 6 εεε Note: The form of the equation is similar to the equation governing gravitation, but the electric force can be either attractive or repulsive. In some situations, which we will deal with in the future, the constant of proportionality k, is written in terms of a different constant ε (more commonly written as ɛ0) The constant Ɛ is called the permitivity of free space. The permitivity of a material (or free space) is related to how well the material resists the flow of charge from one place to another. Study the examples in section 16.6, then do problems Page 497, # 1,3-5,7-11,13-15,19 There will be a short quiz on sections 16.1 - 16.6 in the very near future. Ch. 16 Page 7 16.7 The Electric Field Saturday, July 18, 2015 8:22 PM Rather than deal with a mysterious force at a distance, physicists have developed the idea of a field. Surrounding, or perhaps emanating from every charge, is an electric field. At each point in space the field has a magnitude and a direction (the field is a vector field). When one charge sits in the electric field of a second charge the first charge feels the field (size and direction) of the second charge that exists at that point. The interaction is local. The electric field is defined for all the points surrounding a charge as the force exerted on a small positive test charge placed at each point. That is, the electric field vector at each point is Note that we can easily calculate the electric field strength around an isolated point charge Q. Using Coulomb's Law If there is an array of point charges we can calculate the electric Ch. 16 Page 8 If there is an array of point charges we can calculate the electric force on any single charge by calculating the vector sum of the electric forces of each of the other charges on that single charge. Ch. 16 Page 9 16-8 Electric Field Lines Sunday, July 19, 2015 8:07 PM The electric field is a field of vector quantities. We can represent the field by drawing arrows at all points in the field: the arrow will point in the direction of the field at each point, and have a length proportional to the field strength at each point. Drawing the many arrows required to show the size/shape of the electric field can be messy so we often draw "field lines" instead. Electric field lines are analogous to the magnetic field lines. Magnetic field lines can be demonstrated by sprinkling iron filings over a paper which is placed on top of a magnet. Electric field lines can be demonstrated putting a large number of compasses around an electric charges. The compasses will orient as if there were continuous lines of force from one charge (+) to another (-). Field lines (the lines of electric force) are drawn with these conventions: Field line connect positive and negative charges (though sometimes charges are not drawn but are understood to exist somewhere off the diagram). At each point the tangent to a field line is the direction of the electric field at that point. The size of the electric field is proportional to the number of field lines in that area (volume). [More accurately the electric field strength is proportional to the number of lines crossing a unit area, perpendicular to the lines.] The direction of the field lines at a given point is the direction that a positive test charge would move if placed at that point in the field. In particular, field lines originate on positive charges and terminate on negative charges -- a positive test charge Ch. 16 Page 10 and terminate on negative charges -- a positive test charge moves away from positive charges and towards negative charges. Do problems: Page 498, # 21-25,27,29,31,33,35 Ch. 16 Page 11 16-9 Electric Fields and Conductors Monday, July 20, 2015 1:20 PM If an electric charge (i.e. a surplus of electrons) is placed on a conducting object the electrons will repel one another and distribute themselves until the net force on each electron is zero. Once stability is reached the electric field at every point must be perpendicular to the surface (otherwise the electrons would continue to migrate). Suppose a net positive charge is inside a metallic spherical shell. Electrons in the shell will move to the inner surface of the shell (lines of force originating on the central positive charge must terminate on electrons). But that means there is a net positive charge on the outer surface of the shell and this in turn means there will be lines of force originating on those charges and terminating on electrons somewhere outside the shell. That is there is an electric field in the central hollow part of the shell, and there is an electric field outside the shell, but no electric field in the material of the shell itself. If a hollow metal box is placed in an electric field (i.e placed in a place where lines of force are directed from positive charges to negative charges) the field inside the box will be zero. The positive charges on one side of the box will attract the free electrons in the metal of the box, pulling them to one side, but thus producing a less than normal number of electrons on the other side of the box. Hence there will be lines of force from those positive charges in the box to the negative charges that were responsible for the original field. But there is no charge inside the box. Because free electrons are not available to move around in Ch. 16 Page 12 Because free electrons are not available to move around in non-conductors, electric fields can and do exist in nonconducting materials. As well, the electric field at the surface of non-conductors is not necessarily perpendicular to the surface. Ch. 16 Page 13