Electrostatics. 3) positive object: lack of electrons negative object: excess of electrons

Transcription

1 Electostatics IB 12 1) electic chage: 2 types of electic chage: positive and negative 2) chaging by fiction: tansfe of electons fom one object to anothe 3) positive object: lack of electons negative object: excess of electons 4) Types of mateials: a) Conductos: mateials in which electic chages move feely (e.g. metals, gaphite) b) Insulatos: mateials in which electic chages do not move feely (e.g. plastic, ubbe, dy wood, glass, ceamic) c) Semiconductos: mateials with electical popeties between those of conductos and insulatos (e.g. silicon) d) Supeconductos: mateials in which electical chages move without esistance (e.g. some ceamics at vey low tempeatues) opeties of Atomic aticles e = elementay unit of chage (magnitude of chage on electon) aticle Mass Electic Chage Electon oton m e = x kg m p = x kg q = -e q = x C q = +e q = x C e = 1.60 x C Neuton m n = x kg q = 0 q = 0 C 1. A balloon has gained 2500 electons afte being ubbed with wool. What is the chage on the balloon? What is the chage on the wool? q = -4.0 x C q = +4.0 x C 2. A ubbe od acquies a chage of -4.5 μc. How many excess electons does this epesent? x e Consevation of Electic Chage: The total electic chage of an isolated system emains constant. 1

2 Electic Foce (Electostatic Foce, Coulomb Foce) IB 12 Coulomb s Law: The electic foce between two point chages is diectly popotional to the poduct of the two chages and invesely popotional to squae of the distance between them, and diected along the line joining the two chages. Coulomb Foce F e qq = k k = Coulomb constant (electostatic constant) k = 8.99 x 10 9 N m 2 C -2 NOTE: +-F denotes diection of foce not sign of chage oint chage: a chaged object that acts as if all its chage is concentated at a single point Altenate fomula fo Coulomb foce: F F e e = = 1 qq 4πε 0 qq 4πε k = 1/ 4πε 0 ε 0 = pemittivity of fee space = 8.85 x C 2 N -1 m -2 Use the Coulomb foce to estimate the speed of the electon in a hydogen atom. 2

3 The inciple of Supeposition IB 12 The net electic foce acting on a chaged paticle is the vecto sum of all the electic foces acting on it. 1. Detemine the net electostatic foce on chage q 1, as shown below. 2. Whee can a thid chage of +1.0 µc be placed so that the net foce acting on it is zeo? 3. Thee point chages of -2.0 µc ae aanged as shown. Detemine the magnitude and diection of the net foce on chage q 1. D = 2/3 m 3

4 Electic Field IB 12 Electic field: a egion in space suounding a chaged object in which a second chaged object expeiences an electic foce Test chage: a small positive chage used to test an electic field Electic Field Diagams 1. ositively chaged sphee 2. ositive point chage 3. Negative point chage Radial Field: field lines ae extensions of adii 5. Two positive chages 6. Two negative chages 7. Two unlike chages 8. Oppositely chaged paallel plates Unifom Field: field has same intensity at all spots Edge Effect: bowing of field lines at edges opeties of Electic Field Lines 1. Neve coss 2. Show the diection of foce on a small positive test chage 3. Out of positive, into negative 4. Diection of electic field is tangent to the field lines 5. Density of field lines is popotional to field stength (density = intensity) 6. ependicula to suface 7. Most intense nea shap points 4

5 Electic Field Stength IB 12 Electic Field Stength (Intensity): electic foce exeted pe unit chage on a small positive test chage Electic Field: E = Units: N/C F e q Electic Foce: Fe = Units: N Eq E Electic Field fo a oint Chage: Qq k 2 Q 1 = = k = q 4πε Q oint Chage Spheical Conducto 1. a) Find the magnitude and diection of the electic field at a spot mete away fom a sphee whose chage is micocoulombs and whose adius is 0.60 centimetes. 2. a) Find the magnitude and diection of the gavitational field at an altitude of 100 km above the suface of the Eath. b) Find the magnitude and diection of the electic foce acting on a nc chage placed at this spot. b) Find the magnitude and diection of the gavitational foce exeted on a 6.0 kg bowling ball placed at this spot. c) Find the electic field stength at the suface of the sphee. c) Find the gavitational field stength at the suface of the Eath. 5

6 3. a) Find the magnitude and diection of the net electic field halfway between the two chages shown below. IB 12 b) Detemine the electic foce on a poton placed at this spot. 4. Two chaged objects, A and B, each contibute as follows to the net electic field at point : E A = 3.00 N/C diected to the ight, and E B = downwad. What is the net electic field at? E = 3.61 N/C Theta = a) Two positive point chages, q 1 = +16 μc and q 2 = +4.0 μc, ae sepaated in a vacuum by a distance of 3.0 m. Find the spot on the line between the chages whee the net electic field is zeo. 6

7 6. A poton is eleased fom est nea the positive plate. The distance between the plates is 3.0 mm and the stength of the electic field is 4.0 x 10 3 N/C. IB 12 a) Descibe the motion of the poton. constant acceleation in a staight line b) Wite an expession fo the acceleation of the poton. c) Find the time it takes the poton to each the negative plate. d) Find the speed of the poton when it eaches the negative plate. 7. A paticle is shot with an initial speed though the two paallel plates as shown. a) Sketch and descibe the path it will take if it is a poton, an electon, o a neuton. b) Which paticle will expeience a geate foce? c) Which paticle will expeience a geate acceleation? d) Which paticle will expeience a geate displacement? 8. In the figue, an electon entes the lowe left side of a paallel plate capacito and exits at the uppe ight side. The initial speed of the electon is m/s. The plates ae 3.50 cm long and ae sepaated by cm. Assume that the electic field between the plates is unifom eveywhee and find its magnitude. 7

8 Electic otential Enegy IB 12 High amount of E Gavitational otential Enegy (E ) Reason fo E : 1. Test object has mass (test mass = m) 2. Test mass is in a gavitational field (g) caused by lage object (M) Low amount of E 3. Lage object exets a gavitational foce on test mass (F g = mg) 4. Test mass has tendency to move to base level due to foce 5. Wok done moving object between two positions is path independent. Base level whee E = 0 Gavitational potential enegy: E = mgh W = ΔE = mg Δh Electic otential Enegy (E ) Reason fo E : High amount of E 1. Test object has chage (test chage = +q) 2. Test chage is in an electic field caused by lage object (Q) 3. Lage object exets an electic foce on test chage (F E = Eq) Low amount of E 4. Test chage has tendency to move to base level due to foce 5. Wok done moving object between two positions is path independent. Base level whee E = 0 Electic potential enegy: E = Eq h W = ΔE = Eq Δh Electic otential Enegy (E )- the wok done in binging a small positive test chage in fom infinity to that point in the electic field Deivation fo oint Chages (Wok done by field) E = W = Fscosθ E E E E = EqΔs kq = ( q) ds 2 s kqq = s kqq = E = 0 Electic otential Enegy due to a point chage Fomula: Units: Type: E kqq = J scala 8

9 IB 12 Electic otential (V) - wok done pe unit chage moving a small positive test chage in fom infinity to a point in an electic field. Electic otential due to a point chage Fomula: V V E q = = kq = = kqq q Q 4πε 0 E = qv Units: J/C = volts(v) Type: scala Highe potential B A Lowe potential Zeo potential Lowe potential Highe potential Zeo potential B A 1. a) Calculate the potential at a point 2.50 cm away fom a +4.8 μc chage. b) How much potential enegy will an electon have if it is at this spot? 3. What is the potential whee a poton is placed 0.96 m fom a -1.2 nc chage? 9

10 oint Chages IB 12 +Q +Q +Q +Q Electic Foce Electic Field Electic otential Enegy Electic otential Two objects needed inteaction between the two One object needed popety of that one object Two objects needed quantity possessed by the system One object needed popety of the field Magnitude: F = Eq Magnitude: E = F/q Magnitude: E = qv Magnitude: V = E /q F = kqq/ 2 E = kq/ 2 E = kqq/ V = kq/ Units: N Units: N/C Units: J Units: J/C Type: vecto Type: vecto Type: scala (+/-) Type: scala (+/-) Diection: likes epel, unlikes attact Diection: away fom positive, towads negative Sign: use signs of Q and q Sign: use sign of Q Sign: don t use when calculating check fame of efeence Sign: don t use when calculating check fame of efeence F = 0 whee E = 0 E = 0 whee V = 0 10

11 IB a) Calculate the net electic field at each spot (A and B): b) Calculate the net electic foce on a poton placed at each spot. 2. a) Calculate the net electic potential at each spot (A and B): b) Calculate the electic potential enegy of a poton placed at each spot. 11

12 Electic otential and Conductos Gaphs fo a spheical conducto IB 12 Fo a hollow o solid conducto, 1. all the chage esides on the outside suface 2. the electic field is zeo eveywhee within 3. the extenal electic field acts as if all the chage is concentated at the cente Electic Field Stength Value at suface = kq/ 2 Electic otential 4. the electic potential is constant ( 0) eveywhee within and equal to the potential at the suface adius Distance adius Distance A spheical conducting suface whose adius is 0.75 m has a net chage of +4.8 μc. a) What is the electic field at the cente of the sphee? b) What is the electic field at the suface of the sphee? c) What is the electic field at a distance of 0.75 m fom the suface of the sphee? d) What is the electic potential at the suface of the sphee? e) What is the electic potential at the cente of the sphee? f) What is the electic potential at a distance of 0.75 m fom the suface of the sphee? 12

13 Equipotential Sufaces IB 12 Equipotential suface: a suface on which the electic potential is the same eveywhee 1. Locate points that ae at the same electic potential aound each of the point chages shown. 2. Sketch in the electic field lines fo each point chage. 3. What is the elationship between the electic field lines and the equipotential sufaces? ependicula Field lines point in diection of deceasing potential Electic otential Gadient The electic field stength is the negative of the electic potential gadient. Fomula: Units: N/c o V/m ΔV E = Δ x Fo each electic field shown, sketch in equipotential sufaces. Sketch in equipotential sufaces fo the two configuations of point chages below

14 Electic otential Diffeence IB 12 Electic otential Diffeence (ΔV) wok done pe unit chage moving a small positive test chage between two points in an electic field Fomula: Units: J/C = V W Δ V = q Δ V = ΔE q Δ E = qδv High and Low otential 1. a) Which plate is at a highe electic potential? positive b) Which plate is at a lowe electic potential? negative c) What is the electic potential of each plate? Abitay elative to base level d) What is the potential diffeence between the plates? Not abitay depends on chage, distance between, stength of electic field, geomety of plates, etc. e) Whee will: a poton have the most electic potential enegy? Mak plates with example potentials, as well as spots within field Mak gound mak equipotentials an electon? a neuton? an alpha paticle? Not abitay 2. An electon is eleased fom est nea the negative plate and allowed to acceleate until it hits the positive plate. The distance between the plates is 2.00 cm and the potential diffeence between them is 100. volts. a) Calculate how fast the electon stikes the positive plate. E o = E f E e = E K qv = ½ mv 2 v = sqt (2qV/m) v = sqt(2(1.6 x )(100 V) /(9.11 x )) v = 5.9 x 10 6 m/s b) Calculate the stength of the electic field. Fomula: qv = ½ mv 2 Ve = ½ mv 2 Fomula: E = -ΔV/Δx E = V/d 14

15 The Electonvolt IB 12 Electonvolt: enegy gained by an electon moving though a potential diffeence of one volt Deivation: ΔE e = qδv ΔE e = (1e)(1 V) = 1 ev ΔE e = (1.6 x C)( 1 V) ΔE e = 1.6 x J Theefoe: 1 ev = 1.60 x J 1. How much enegy is gained by a poton moving though a potential diffeence of 150. V? 150 ev o 150(1.60 x ) = 2.4 x J 2. A chaged paticle has 5.4 x J of enegy. How many electonvolts of enegy is this? Facto-label (5.4 x J) (1 ev/1.6 x ) = 3375 ev 3. An electon gains 200 ev acceleating fom est in a unifom electic field of 150 N/C. Calculate the final speed of the electon. 4. In Ruthefod s famous scatteing expeiments (which led to the planetay model of the atom), alpha paticles wee fied towad a gold nucleus with chage +79e. An alpha paticle, initially vey fa fom the gold nucleus, is fied at m/s diectly towad the gold nucleus. Assume the gold nucleus emains stationay. How close does the alpha paticle get to the gold nucleus befoe tuning aound? (the distance of closest appoach ) 2.74 x m 15