Chapter Sixteen: Electric Charge and Electric Fields

Transcription

1 Chapte Sixteen: Electic Chage and Electic Fields Key Tems Chage Conducto The fundamental electical popety to which the mutual attactions o epulsions between electons and potons ae attibuted. Any mateial though which heat and o electical chage can be tansfeed. Mateials, usually metals, though which electons can flow. Good conductos of heat ae geneally good conductos of electicity. Consevation of Chage The pinciple that electic chage is neithe ceated no destoyed but it tansfeable fom one mateial to anothe. Coulomb Coulomb s Law Electical Foce SI unit of chage. One coulomb (symbol C) is equal to the total chage of electons. The elationship between electical foce, chages, and distance: The electical foce between two chages vaies diectly as the poduct of the chages and invesely as the squae of the distance between them. A foce that one chage exets on anothe. When the chages ae the same sign, they epel; when the chages ae opposite, they attact. Electically Polaised Tem applied to an atom o molecule in which the chages ae sepaated so that one side is slightly moe positive o negative than the opposite side. Electostatics The study of electic chages at est. Eathing / Gounding Allowing chages to move feely along a connection between a conducto and the gound o eath. Induction of Chage Insulato Supeconducto Electic Field The chaging of an object without diect contact with anothe chaged body. A mateial that is a poo conducto of heat and also a mateial that is a poo conducto of electicity. Mateial that has infinite conductivity at vey low tempeatues, so that chage flows though it without esistance. exists in a space suounding a chaged paticle o object. Electic fields ae epesented by lines of foce that stat on a positive chage and end on a negative chage. (Measued by foce/chage - N/C), Physics, 5 th Edition Chapte Sixteen: Electic Chage & Electic Fields Page of

2 Electostatics Electostatics is concened with electic chages at est. Concept of the Atom Potons Neutons Electons Chage Neutons Positive cental nucleus (no chage) Nucleus suounded by negatively chaged electons. Potons Nucleus composed of potons and (positive chage) neutons. Electons Mass of poton 000 time mass of an (negative chage) electon. Neuton slightly moe massive than a poton. - positively chaged - no chage - negatively chaged Lie chages Repel Unlie chages Attact Chage is the electical popety to which the attaction and epulsion of potons and electons is attibuted. Chage is measued in coulombs (C). Fo example an electon has a chage of C. Consevation of Chage The outemost electons ae loosely bound to the atom and ae elatively easily dislodged. Hence when thee is fiction (ubbing), thee is a tansfe of electons. An imbalance of electons esults in a net electic chage. An excess of electons yields a net negative chage. A deficiency of electons yields a net positive chage. Electons ae not ceated o destoyed, they ae simply tansfeed. Chage is conseved. Conductos have vey loosely bound electons Sea of Electons which ae in a lattice of positive ions. eg. metals. Insulatos have tightly bound electons that emain with paticula atoms. eg. plastics, ubbe., Physics, 5 th Edition Chapte Sixteen: Electic Chage & Electic Fields Page of

3 Coulomb s Law F Recall Newton s Law of Gavitation whee G is the univesal gavitational constant. This foce is attactive and along the line joining the two point masses m and m. The electical foce between any two objects obeys a simila invese-squae elationship with distance. Coulomb s Law states that fo chaged paticles the foce between the chages vaies diectly as the poduct of the chages and invesely as the squae of the distance between them. F whee epesents the chage of one paticle epesents the chage of the othe paticle d is the distance between the chage paticles. popotionality constant Nm /C (SI units) 4 πε 0 (ε 0 pemittivity of fee space) Note: Fee space is consideed to be a vacuum. The value of the constant of pemittivity is only slightly diffeent in ai and we shall ignoe this diffeence. This equation gives the magnitude of the electic foce that eithe object exets on the othe, when the magnitudes of the chages and ae given. The diection of the electic foce is always along the line joining the two chaged paticles. If two chages have: same sign opposite sign d G m d the foce on eithe object is diected away fom the othe. ie. epulsion occus. foce on one is diected towads the othe. ie. attaction occus. m, Physics, 5 th Edition Chapte Sixteen: Electic Chage & Electic Fields Page 3 of

4 Note that the foce the fist chage exets on the second is equal but opposite to that exeted by the second on the fist (Newton s Thid Law). Note: Coulomb s Law equation gives the foce on a chage due to only one othe chage. If seveal (o many) chages ae pesent, the net foce on any one of them will be the vecto sum of the foces due to each of the othes (Electic foces add as vectos). This is sometimes efeed to as the pinciple of supeposition of foces. F F + F +... net n F n The magnitude of the foce can be calculated using Coulomb s Law. The diection is along the line joining the chages (attaction o epulsion depending on the natue of the chages: lie chages epel, unlie attact). Thee Chages in a Line (This comes diectly fom Example 6-3 in ) Thee chaged paticles ae aanged in a line, as shown. Calculate the net electostatic foce on paticle 3 (-4.0µC) due to the othe two chages. Solution The net foce on paticle 3 will be the vecto sum of the foce F 3 exeted by paticle and the foce F 3 exeted by paticle : F F 3 + F 3. The magnitudes of these two foces ae: F F 3 3 ( ( Nm Nm /C /C )( ( 0. 50m) )( ( 0. 0 m) 6 6 C)( C)( C) C). N. 7N, Physics, 5 th Edition Chapte Sixteen: Electic Chage & Electic Fields Page 4 of

5 Since we wee calculating the magnitudes of the foces, we omitted the signs of the chages; but we must be awae of them to get the diection of each foce. Let the line joining the paticles be the x-axis, and we tae it positive to the ight. Then, because F 3 is epulsive and F 3 is attactive, the diections of the foces ae as shown below: F 3 points in the positive x diection and F 3 points in the negative x diection. The net foce on paticle 3 is then F 3 F3 + F. 7 N +. N. 5N The magnitude of the net foce is.5n, and it points to the left. Electic Field Contact Foce Foce Field is a common foce whee contact is made by a push o pull. eg. pushing a ca o hitting a softball. is a concept of a foce acting at a distance. Both gavitational and electical foce act at a distance. The space is said to contain a foce field theefoe the mass o chage is in contact (inteacts) with the field all the time. An electic field suounds evey chaged body in space. When a second chage is placed nea the fist chage, it feels a foce because of this electic field. We can investigate the electic field suounding a chage o a goup of chages by measuing the foce on a small positive test chage. Electic field is defined in tems of the foce on a small positive test chage. E (Electic Field) F (foce) q (foce pe unit chage) (Newtons/Coulomb) diection is the diection of the foce on a small positive test chage. E is a vecto quantity., Physics, 5 th Edition Chapte Sixteen: Electic Chage & Electic Fields Page 5 of

6 The electic field due to a single point chage can be witten (whee q is a small positive test chage placed at a distance fom chage ) E F q q q 4 πε Electic Field of a Single Point Chage (This comes diectly fom Example 6-6 in ) Calculate the magnitude and diection of the electic field at a point P which is 30cm to the ight of a point chage C. Solution The magnitude of the electic field due to a single point chage is given by: E 9 6 ( Nm /C )( C ) ( m ) The diection of the electic field is towad the chage as shown in (a) below since we defined the diection as that of the foce on a positive test chage. If had been positive, the electic field would have pointed away, as in shown in (b) below. If the field is due to moe than one chage, the individual electic fields (E, E, ) due to each chage ae added vectoially to get the total field at any point (supeposition pinciple). E E E N/C, Physics, 5 th Edition Chapte Sixteen: Electic Chage & Electic Fields Page 6 of

7 E at a Position Between Two Point Chages (This comes diectly fom Example 6-7 in ) Two point chages ae sepaated by a distance of 0.0cm. One has a chage of - 5µC and the othe +50µC. (a) What is the diection and magnitude of the electic field at a point P in between them, that is.0cm fom the negative chage? The field will be a vecto sum of two fields both pointing to the left: the field due to the negative chage points towad, and the field due to the positive chage points away fom, again to the left. Thus we can add the magnitudes of the two fields togethe algebaically, ignoing the signs of the chages: E whee in the last step we factoed out ( / ). We substitute in.0cm m and m: E ( ) ( ( ) ) C 9 0 Nm C m [ + ] NC NC 8 + ( 50 5) ( ) Notice how factoing out / on the fist line allowed us to see the elative stengths of the two contibuting fields, namely that s field is only / 8 of s (o / 9 of the total). (b) If an electon is placed at est at P, what will its acceleation a be? Give both magnitude and diection fo a. The electon will feel a foce to the ight since it is negatively chaged and the acceleation will theefoe be to the ight, with a magnitude of: Note: 9 8 ( C)( NC ) 0 F qe a. 0 3 m m 9. 0 g If we ae given the electic field E at a given point in space then we can calculate the foce F on a chage q: F q E ms, Physics, 5 th Edition Chapte Sixteen: Electic Chage & Electic Fields Page 7 of

8 Electic Field Lines (Line of Foce) A seies of lines ae dawn to indicate the diection of the electic field at vaious points in space. Each line epesents the diection of the electic field. Only a few epesentative lines ae dawn. The close the lines ae togethe, the stonge the electic field in that egion. If the field line is cuved, E is epesented by a tangent to that cuve. Electic field lines stat on positive chages and end on negative chages. The field lines between chaged paallel plates ae equally spaced (except nea the edges) so E has the same magnitude at all points (Econstant)., Physics, 5 th Edition Chapte Sixteen: Electic Chage & Electic Fields Page 8 of

9 Electic Fields and Conductos The electic field inside a hollow conducto is exactly zeo, even if it is chaged. If the metal sphee is chaged, because of mutual epulsion, the electons have spead as fa apat as possible and distibute themselves unifomly ove the suface of the sphee. The foces on a positive test chage located inside a chaged hollow sphee cancel to zeo. If the conducto is not spheical, then the chage distibution will not be unifom. Fo example, in a cube most of the chage is located nea the cones. The exact chage distibution ove the sufaces and cones of all hollow conductos is such that the electic field eveywhee inside the conducto is zeo. On an iegula shaped conducto, the chage tends to accumulate at locations whee the adius of cuvatue of suface is smallest (at the shap points o edges). Static chages ae distibuted on the suface of all conductos in such a way that the electic field inside the conductos is zeo The electic field outside a conducto is always pependicula to the suface at any point., Physics, 5 th Edition Chapte Sixteen: Electic Chage & Electic Fields Page 9 of

10 APPLICATION: PHOTOCOPIER Photocopies and lase pintes employ simila pinciples and povide a vey good example of the application of electic fields. They ae devices that pint copies of documents, dawings etc fom an optical image to a sheet of copy pape. Ionisation of the ai by electic fields. When the ai is exposed to an electic field, the (few) ions, which natually occu in the ai, ae acceleated in the diection of the field until they collide with neutal gas molecules. If the electic field is lage enough then the ions will have sufficient enegy to ionise the molecules, poducing additional ions and electons. The esultant chaged paticles ae then acceleated and collide with othe neutal molecules theeby poducing moe ionisation. Coona Dischage Electic fields lage enough to ionise the ai can be poduced using a shap point, o by applying a high voltage lage than seveal V to a smalle wie as in a photocopie. Shap points ae commonly used as lightning ods to emove the chaged paticles fom the ai and thus pevent the lightning fom stiing the object to which the od is attached. A Coona Dischage can be poduced by sticing a needle onto the dome of a Van de Gaaff geneato. The flow of ions (fom the point) can be seen to deflect a candle flame o a piece of pape held vetically., Physics, 5 th Edition Chapte Sixteen: Electic Chage & Electic Fields Page 0 of

11 A Coona Dischage is a esult of a net movement of many positively and negatively chaged paticles in opposite diection to the electic field. (+ve tavel in same diection as E and -ve tavel in opposite diection to E) Non-conducting (often called dielectics) mateials, ae polaised when placed in electic field ie individual paticles loo lie diagams below: No field E- Field (diection ) Thee is a sepaation of chage in paticles when E is vey high, the ve chages (electons) and the +ve chaged ions ae sepaated and then the mateial (solid, liquid o gas) becomes ionised. Recombination and othe chemical pocesses occu esulting in enegy being given out, often in the fom of heat, light o sound. The light is bluish o eddish depending on the ions pesent and a coloued luminous glow suounds the conducto called a Coona Dischage. A Photoconductive Suface is a mateial that is a poo conducto of electicity in the da but becomes a easonably good conducto when exposed to light. THE PROCESS: The photoconductive suface is given a positive electostatic chage in the da. A thin coona wie, which extends ove the full length of a dum and chages the photoconductive suface placed on this dum do this. The chage is positive and distibuted unifomly as the dum otates unde the wie. The page to be copied is then pojected onto the chaged suface. The photoconducting suface becomes conducting only in aeas whee the light sties (ie whee the light poduces chage caies on the photoconductive suface theefoe neutalising the positive chages suface.) Since the chages emain on those egions of the photoconductive suface not exposed to the light a hidden image of the object is now in the fom of a positive suface chage distibution. This suface is then coveed with a negatively chaged powde, a tone, which adhees only to the positively chaged image aea. This image is then tansfeed to the suface of a sheet of pape, which is positively chaged and then finally fixed by heat (melted). This then povides a pemanent copy of the oiginal.. Conside Summay (p.496). Sample uestions Activities 3. uestions (p.496,497: no.5, 9, 0, 9) 4. Poblems (p.497,498: no.,, 3, 5, 6, 7,, 3, 4, 5), Physics, 5 th Edition Chapte Sixteen: Electic Chage & Electic Fields Page of