PHY002 Lecture Notes for PreDegree Science


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1 PHY00 Lectue Notes fo PeDegee Science Couse Contents: Magnets, Magnetic fields and Electostatic By Odusote Y. A Depatment of Physics Fedeal Univesity of Technology P. M.B. 704, Akue, Ondo State. 1
2 MAGNETS AND MAGNETIC FIELDS Definitions: A magnet has two poles Noth (N) and South (S). A pemanent magnet is a piece of feomagnetic mateial (such as ion, nickel o cobalt) which has popeties of attacting othe pieces of these mateials. A pemanent magnet will position itself in a noth and south diection when feely suspended. The nothseeking end of the magnet is called the Noth pole, N, and the southseeking end the South pole, S. If a ba magnet is suspended fom its midpoint and can swing feely in a hoizontal plane, it will otate until its noth pole points to the Eath s geogaphic Noth Pole and its south pole points to the Eath s geogaphic South Pole. (The same idea is used in the constuction of a simple compass) i.e. when suspended feely N shows noth and S shows south. The aea aound a magnet is called the magnet field and it is in this aea that the effects of the magnetic foce poduced by the magnet can be detected. A magnetic field cannot be seen, felt, smelt o head and theefoe is difficult to epesent. Michael Faaday suggested that the magnetic field could be epesented pictoially, by imaging the field to consist of lines of magnetic flux, which enables investigation of the distibution and density of the field to be caied out.(see Fig.1) Fig. 1: Showing lines of magnetic flux The distibution of a magnetic field can be investigated by using some ion fillings. A ba magnet is placed on a flat suface coveed by, say, cadboad, upon which is spinkled some ion fillings. If the cadboad is gently tapped the fillings will assume a patten simila to that shown in Fig. (a, b,c) below. If a numbe of magnets of diffeent stength ae used, it is found that the stonge the fields the close ae the lines of magnetic flux and vicevesa. Thus a magnet field has the popety of exeting a foce, demonstated in this case by causing the ion fillings to move into the patten shown. The stength of the magnetic field deceases as we move away fom the magnet.
3 Fig. (a) Magnetic field patten suounding a ba magnet as displayed with ion filings. (b) Magnetic field patten between unlike poles of two ba magnets. (c) Magnetic field patten between like poles of two ba magnets. It should be noted that: Poles always exist in pais; Thee is no magnetic monopoles; (All attempts thus fa to detect an isolated magnetic pole have been unsuccessful. No matte how many times a pemanent magnet is cut in two, each piece always has a noth and a south pole.) Poles of a magnet have the same stength; Like poles epels, unlike poles attact each othe. Fig. 3: when a magnet is boken into half Mateials attacted by a magnet is called magnetic e.g. Ion, Nickel, while mateials not attacted by a magnet is called nonmagnetic e.g. wood, plastic. A compass is a navigational instument fo finding diections. It consists of a magnetised pointe fee to align itself accuately with Eath's magnetic field. A compass povides a known efeence diection which is of geat assistance in navigation. The cadinal points ae noth, south, east and west. A compass can be used in conjunction with a clock and a sextant to povide a vey accuate navigation capability. This device geatly impoved maitime tade by making tavel safe and moe efficient. 3
4 A compass can be any magnetic device using a needle to indicate the diection of the magnetic noth of a planet's magnetosphee. Any instument with a magnetized ba o needle tuning feely upon a pivot and pointing in a nothely and southely diection can be consideed a compass. Magnetic Flux and Flux Density Magnetic flux is the amount of magnetic field (o the numbe of lines of foce) poduced by a magnetic souce. The symbol fo magnetic flux is ϕ. The unit of magnetic flux is the Webe (Wb). Magnetic flux density is the amount of flux passing though a defined aea that is pependicula to the diection of the flux. magneticflux φ Magnetic flux density, B = = (unit Tesla,T) aea A The SI unit of magnetic field is the newton pe coulombmete pe second, which is called the tesla (T): whee 1T = 1Wb/m ; A(m ) is the aea. Also thee is Gauss(G): 1T = 10 4 G Example 1: A magnetic pole face has a ectangula section having dimensions 00mm by 100mm. If the total flux emeging fom the pole is 150µWb, calculate the flux density. Solution: Aea, A = 00mm x100mm = 0,000mm =0,000 x 106 m. Magnetic flux, = 150µWb = 150 x 106 Wb 6 150x10 B = φ = = T = 7.5mT 6 A 0000x10 Magnetic field of the eath The eath is a giant magnet itself. The geogaphical pole and magnetic pole ae not at the same place. Declination angle is between geogaphical and magnetic noth.(see Fig.4) Inclination angle is between the magnet needle and hoizontal. (Inclination angle is zeo only at the magnetic equato). The magnetic field of the eath is about 105 T. 4
5 Fig. 4: The Eath s magnetic field lines. Note that a south magnetic pole is nea the noth geogaphic pole, and a noth magnetic pole is nea the south geogaphic pole. What is Electostatic? Electostatics is the study of electic chage which is not moving i.e. is static. Chage All objects suounding us (including people!) contain lage amounts of electic chage. Chage can be negative o positive and is measued in units called coulombs (C). Usually, objects contain the same amount of positive and negative chage so its effect is not noticeable and the object is called electically neutal. Howeve, if a small imbalance is ceated (i.e. thee is a little bit moe of one type of chage than the othe on the object) then the object is said to be electically chaged. Some athe amusing examples of what happens when a peson becomes chaged ae fo example when you chage you hai by combing it with a plastic comb and it stands ight up on end! Anothe example is when you walk fast ove a nylon capet and then touch a metal dooknob and give youself a small shock (altenatively you can touch you fiend and shock them!) Electic Chages: Poduction, types and stoage of chages In so many cases when two objects ae ubbed against each othe, they become chaged and they ae said to posses ELECTRIC CHARGES. Examples ae ubbing a piece of had ubbe, a glass od o a plastic with a cloth. The amount of chage tansfeed depends on the type of mateials and the intensity of the ubbing. Thee is attaction when two balls suspended close to each othe, one touch by the glass od and the othe by the cloth (this is obseved if the glass od and the cloth have been ubbed togethe befoe). When the two balls ae touched by the same objects (glass od o cloth) thee is epulsion (Fig. 5). 5
6 Fig. 5: Attaction and Repulsion Phenomenon. What actually happens is that when you ub the glass with silk, tiny amounts of negative chage ae tansfeed fom the glass onto the silk, which causes the glass to have less negative chage than positive chage, making it positively chaged. When you ub the plastic od with the fu, you tansfe tiny amounts of negative chage onto the od and so it has moe negative chage than positive chage on it, making it negatively chaged. Fom this evidence, Chales du Fay in 1733 concluded thee ae two kinds of chage, which he called Electic fluid. As we can see fom above like chages epel, and unlike chages attact. The electic fluid on glass was named viteous, while that on cloth was named esinous. He believed that these fluids wee sepaated by the fiction involved in ubbing. Howeve, aound 1750, Benjamin Fanklin poposed the flow of a single fluid fom one body to the othe duing the pocess of ubbing. Positive chages was associated with the body that gains fluid and negative to the body that loses fluid (this convention still stands till today). PROPERTIES OF ELECTRIC CHARGE Electic chage and electic foces play a majo ole in detemining the behaviou of the univese. The basis building blocks of matte, electons and potons, have a popety called electic chage. Electic chage is obseved to have the following chaacteistics: (i) An electic chage has a polaity; that is, it is eithe positive o negative. Like chages epel each othe, and opposite (unlike) chages attact. (ii) The foce between chages is popotional to thei magnitudes and vaies as the invese squae of thei sepaation. (iii) An electic chage is conseved. It cannot be ceated o destoyed. We obtain chages by sepaating neutal objects into a negative piece and a positive piece. (iv) An electic chage is quantized. Not until 19 th centuy electical chage was consideed to be continuous. Expeiments have shown that electical chage is quantized (i.e. appeas only in discete amounts). It is always obseved to occu as an intege multiple of e, the fundamental quantity of chage. We choose the unit of electic unit of electic chage as the Coulomb, whee e = 1.60 x Coulomb (C). The chage on the electon is e, and on a poton +e. Conductos ae mateials in which chage can move elatively feely and in which thee ae some fee chages. Examples of good conductos ae metals, plasmas (ionized gases), liquids containing ions (fo examples, sulfuic acid, blood, salt wate), and some semiconductos. Insulatos ae mateials that do not eadily tanspot chage. Examples ae a vacuum, glass, distilled wate, pape and ubbe. Thee is not a shap demacation between conductos and insulatos. Some 6
7 mateials (fo example, Semiconductos like Silicon o Gemanium) have popeties intemediate between a good conducto and a good insulato. ELECTRIC CHARGE: WHERE DOES IT ORIGINATE? The electic chage has it oigin within the atom itself. Atoms ae the building blocks of matte. They ae the basis of all the stuctues and oganisms in the univese. The planets, the sun, gass and tees, the ai we beathe, and people ae all made up of atoms. Atoms ae vey small and cannot be seen with the naked eye. They consist of two main pats: the positively chaged nucleus at the cente and the negatively chaged elementay paticles called electons which suound the nucleus in thei obitals. (Elementay paticle means that the electon cannot be boken down to anything smalle and can be thought of as a point paticle.) The nucleus of an atom is made up of a collection of positively chaged potons and neutal paticles called neutons. Atoms ae electically neutal which means that they have the same numbe of negative electons as positive potons. The numbe of potons in an atom is called the atomic numbe which is sometimes also called Z. The atomic numbe is what distinguishes the diffeent chemical elements in the Peiodic table fom each othe. In fact, the elements ae listed on the Peiodic table in ode of thei atomic numbes. Fo example, the fist element, hydogen (H), has one poton wheeas the sixth element, cabon (C) has 6 potons. Atoms with the same numbe of potons (atomic numbe) shae physical popeties and show simila chemical behaviou. The numbe of neutons plus potons in the nucleus is called the atomic mass of the atom. An atoms which has lost an electon is called an ion, i.e. +vely chaged and is thus able to attact an electon to itself fom anothe atom. Electons that move fom one atom to anothe ae called fee electons and such andom motion can continue indefinitely. PRODUCTION OF CHARGES Chages can be poduced by the following two methods Chaging by Induction Chaging by Contact Induction is a method though which an object can be chaged. This pocess of chaging is based on the discovey of John Canton in 1753 that an insulated metal object can be chaged even without connecting it to a chaged body. The pocess of chaging without contact is temed INDUCTION. When a negatively chaged od is bought nea a squae object, it leaves a negative chage at the opposite end of the squae object as shown below (Fig. 6). A chage is said to have been induced at the two ends of the squae object. No chage has been ceated; it has meely sepaated; the net chage on the squae object is still zeo. Howeve, if the metal wee now cut in half, we would have two chaged objects, one positive and one negative. Thee ae two ways of ceating a chaged object, with net chage not equal to zeo, by induction: By chaging two objects which ae initially in contact with each othe (Method 1) By chaging a single object, then eath it fo chage neutalization (Method ). Method 1 Conside two squae objects (1 and ) on an insulating stands and initially in contact (Fig. 6). When a negatively chaged od is bought close to 1, the fee electons in the object ae epelled away fom the od. This epulsion leaves unbalanced positive chage on the left side of object 1, and negative chage on the ight suface of object. The od has induced a chage sepaation. The next step is to sepaate the two objects with the od still pesent. If the od is emoved befoe sepaating the objects, the chage 7
8 sepaation will be lost and the objects will become neutal. The last step is the emoval of the chaged od. The chages caied by the two squae objects ae always equal and opposite. (a) (b) (c) Fig. 6: Two squae objects given equal and opposite chages by the pocess of induction. Method This involves only one squae object. The object is stand on an insulato (Fig. 7). When a negatively chaged od is bought nea, it induces a chage sepaation. The step that follows this is to connect the object to the gound using fo example a wate pipe, while the od is still pesent. (The eath is so lage, it can easily accept o give up electons; hence it acts like a esevoi). Though this connection electon will leave the object to the gound leaving the object positively chaged. The gound connection is then emoved with the od still pesent; because if the od is moved away befoe the connection is emoved, the electons would all have moved back into the object and it would be neutal. (a) (b) (c) (d) Fig. 7: A single squae object chaged by induction. The Electoscope The electoscope is a device fo detecting small amount of chage. An electoscope consists of a tanspaent containe inside of which ae two movable leaves often made of gold. The leaves ae attached by a conducto to a metal ball on the outside of the containe, but ae insulated fom the containe itself. If a positively chaged glass od is bought nea an unchaged electoscope, the electons in the knob ae attacted to the glass od. The motion of these electons bings about an unbalanced positive chage on the leaves, which causes them to epel each othe (Fig. 8a). The leaves will fall back to the vetical position if the od is moved away. 8
9 The knob can also be chaged by conduction, in this case the whole appaatus becomes chaged with the same kind of chage (Fig. 8b). In both the induction and conduction methods of chaging an electoscope, the geate the amount of chage the stonge the epulsion between the leaves. Even, if oughly, it is theefoe clea that an electoscope can be used to measue the amount of chage. Fig. 8: Electoscope chaged by (a) Induction, (b) Conduction (a) The sign of the chage on an object can also be detemined using an electoscope. This can be done by fist chaging the electoscope (positively o negatively) by conduction. Suppose the electoscope is chaged negatively and a negative object is bought close, electons ae induced to move fathe down into the leaves and they sepaate futhe. On the othe hand, if a positive object is bought close, the electons ae induced to flow upwad, leaving the leaves less negative and thei sepaation is educed (Fig. 9). (b) Fig. 9: Detemination of sign of a given chage Coulomb's Law The behaviou of the electostatic foce was studied in detail by Chales Coulomb aound Though his obsevations he was able to show that the electostatic foce between two pointlike chages is invesely popotional to the squae of the distance between the objects. He also discoveed that the foce is popotional to the poduct of the chages on the two objects. Q F α 1 Q whee Q1 is the chage on the one pointlike object, Q is the chage on the second, and is the distance between the two. The magnitude of the electostatic foce between two pointlike chages is given by Coulomb's Law: 9
10 F = k Q Q 1 and the popotionality constant k is called the electostatic constant. We will use the value k = 8:99 x 10 9 N. m /C. The value of the electostatic constant is known to a vey high pecision (9 decimal places). Not many physical constants ae known to as high a degee of accuacy as k. Aside: Notice how simila Coulomb's Law is to the fom of Newton's Univesal Law of Gavitation between two pointlike paticles: F G = G m m 1 whee m 1 and m ae the masses of the two paticles, is the distance between them, and G is the gavitational constant. It is vey inteesting that Coulomb's Law has been shown to be coect no matte how small the distance, no how lage the chage: fo example it still applies inside the atom (ove distances smalle than m). Let's un though a simple example of electostatic foces. Question 1: Two pointlike chages caying chages of +3 x109 C and 5 x 109 C ae m apat. Detemine the magnitude of the foce between them and state whethe it is attactive o epulsive. Solution: Detemine the magnitude of the foce: Using Coulomb's Law we have 9 9 Q 1Q 9 ( + 3 x10 C )( 5 x10 C ) F = k = (8.99 x10 N m / C ) ( m ) = 3.37 x10 8 N Thus the magnitude of the foce is 3:37 x 108 N. The minus sign is a esult of the two point chages having opposite signs. Is the foce attactive o epulsive? Well, since the two chages ae oppositely chaged, the foce is attactive. We can also conclude this fom the fact that Coulomb's Law gives a negative value fo the foce. 10
11 Question : Detemine the electostatic foce and gavitational foce between two electons 1Åapat (i.e. the foces felt inside an atom) Solution: Get eveything into S.I. units: The chage on an electon is x C, the mass of an electon is 9.11 x kg, and 1Å =1 x m. Step 1: Calculate the electostatic foce using Coulomb's Law: Q1Q e. e ( 1.60 x10 C)( 1.60 x10 C F = k = k = (8.99 x10 9N m / C ) 10 (1x10 m) 8 =.30 x10 N Hence the magnitude of the electostatic foce between the electons is.30 x108 N. (Note that the electons cay like chage and fom this we know the foce must be epulsive. Anothe way to see this is that the foce is positive and thus epulsive.) Step : Calculate the gavitational foce: F G m1m = G = 5.54x10 51 me m = G N e = (6.67x10 11 N m 11 / kg 31 (9.11x10 kg)(9.11x10 ) 10 (1x10 m) The magnitude of the gavitational foce between the electons is 5:54 x N. Note that the gavitational foce between the electons is much smalle than the electostatic foce. Fo this eason, the gavitational foce is usually neglected when detemining the foce between two chaged objects. We mentioned above that chage placed on a spheical conducto speads evenly along the suface. As a esult, if we ae fa enough fom the chaged sphee, electostatically, it behaves as a pointlike chage. Thus we can teat spheical conductos (e.g. metallic balls) as pointlike chages, with all the chage acting at the cente. Execises: 1. Find the electic foce that a poton exets on an electon in a hydogen atom. Compae the esult with the gavitational foce between the two. Hints: m 1 = 9.11 x1031 kg; m = 1.67x107 kg; G=6.67x10 11 N m /kg q 1 = 1.6x1019 C; q = +1.6x1019 C; = 0.05nm. What is meant by chage is quantized? 3. Which of the following items will be attacted to the noth pole of a pemanent magnet by a magnetic foce? (A) The noth pole of anothe pemanent magnet (B) A piece of ion that is not a pemanent magnet (C) A positively chaged glass od (D) A negatively chaged ubbe od. Suggested efeences: 1. Univesity Physics W. Seas. Fundamentals of Physics by HallidayResnickWalke 3. Advance level Physics by Nelkon and Pake 4. College Physics by Fedeick, J Beuche and Eugene Hecht 5. College Physics 6edition by Faughn & Seway 31 kg)
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