UNIT 3:Electrostatics

Transcription

1 The study of electic chages at est, the foces between them and the electic fields associated with them. UNIT 3:lectostatics S7 3. lectic Chages and Consevation of chages The electic chage has the following impotant popeties : Thee ae two kinds of chages in natue positive and negative chage. Chages of opposite sign attact one anothe attactive foce. Chages of the same sign epel one anothe epulsive foce. The total chage in an isolated system is constant (conseved Pinciple of consevation of chages Chage is uantized. lectic chage exists as discete packets and witten as ne whee : electic chage n : intege numbe,,... e : fundamental amount of chage,.6 x -9 C S7

2 lectical conductos Definition is defined as the mateials in which some of the electons (negative chages ae fee electons that ae not bound to atoms and can move elatively feely though the mateial. o example : coppe, aluminum, silve and etc lectical insulatos Definition is defined as the mateials in which all electons ae bound to atoms and cannot move feely though the mateial. o example : glass, ubbe, wood and etc... xplanation of conductos and insulatos Conside two metal sphees, one highly chaged and the othe electically neutal (numbe of positive and negative chage ae eual as shown in figue (a. igue (b shows the two sphees connected by a metal nail, which conducts chage (electon fom one sphee to the othe. igue (c shows the two sphees connected by a wood, almost no chage is conducted. S Coulomb s Law States the magnitude of the electostatic (Coulomb/electic foce between two point chages is popotional to the poduct of the chages and invesely popotional to the suae of the distance between them. Mathematically, whee + + k : magnitudeof electostatic (Coulomb foce, : magnitude of chage : distance between two point chages 9 k : electostatic (Coulomb constant 9. x N m S7 4 C -

3 Since k, hence the Coulomb s law can be witten as 4πε 4πε whee ε : pemittivity of ( ε 8. 85x C N m If and ae chages of opposite sign, the foce ( acting on each chage is attactive as shown in figue below. + - fee space (vacuum o ai This mean that is diected towads the neighbouing chage and will esult in both chages moving towads each othe. If and ae both positive o both negative chages, the foce ( acting on each chage is epulsive. This mean that is diected away fom the neighbouing chage and will esult in a sepaation of the two chages if they ae fee to move. Simulation S7 5 Gaphs below show the vaiation of electostatic foce with the distance between two chages. Gadient, M k The S.I. unit of chage is coulomb (C. Coulomb is defined as the total chage tansfeed by a cuent of one ampee in one second. Note : The sign of the chage can be ignoed when substituting into the Coulomb s law euation. The sign of the chages is impotant in distinguishing the diection of the electic foce. S7 6

4 xample : Two point chages, - nc and 9 nc, ae sepaated by a distance of 4. cm as shown in figue below. - + ind the magnitude and diection of a. the electic foce that exets on. b. the electic foce that exets on. (Given Coulomb s constant, k 9. x 9 N m C - Solution:. x -8 C, 9. x -8 C, 4. x - m - + whee 4. cm 4. cm :foce by chage on chage :foce by chage on chage S7 7 a. By applying the Coulomb s law euation : b. By using the Coulomb s law euation : Conclusion : k 9 ( 9. x (. x ( 4x. x N k. x The magnitude of both foces is the same but opposite in diection obey the Newton s thid law. The chaacteistic of electic foce exet on both chages is attactive foce. N 8 ( 9. x 8 Diection : to the left ( Diection : to the ight ( S7 8

5 xample : Thee point chages lie along the x-axis as shown in figue below. C 4 C 3 6 C cm 5. cm Calculate the magnitude and diection of the total electic foce exeted on. (Given Coulomb s constant, k 9. x 9 N m C - Solution: 3. x - m, 3 5. x - m C 4 C 3 6 C cm 5. cm By applying the Coulomb s law euation : k x 8. 3 N Diection : to the ight ( 3 S7 9 k and x N Diection : to the ight ( 3 Theefoe, the total foce exeted on is given by x x x N. xample 3 : igue below shows the thee point chages ae placed in the shape of tiangula. 3 - θ 3-3 Diection : to the ight ( 3 + S7

6 Detemine the magnitude and diection of the esultant electic foce exeted on. Given -. µc, +3.7 µc, µc, 5 cm, 3 cm, θ3 and k 9. x 9 N m C -. Solution:.x -6 C, 3.7x -6 C, 3.3x -6 C, 5x - m, 3 x - m 3 By applying the Coulomb s law euation : Magnitude of : - θ 3 k ( 9. x. 78 N - 3 o (. x ( 5x 6 ( 3. 7 x 6 S7 Magnitude of 3 : k N Constuct a table to epesents x and y-component fo all foces exeted on. oce ecto sum the x-comp. and y-comp. : The magnitude of esultant electic foce exeted on : 3 x-component(n ( ( x + y y-component(n o 3 3 cos58 3 sin 58 o x + 3 cos N o sin 58. N y 3 S N o

7 The diection of esultant electic foce exeted on : tanθ xample 4 : Two identical point chages and B, each of mass g, suspended fom a fixed point O on two insulating theads as shown in figue below. The chages ae in euilibium and each caies the same amount of chage,. If θ, calculate a. the magnitude of both point chages. θ θ b. the magnitude of the electic foce acting on each chage. 5. cm B y x o θ 34. o 35.8 fom the +x-axis (anticlockwise. (Given ε 8.85 x - C N - m - S7 3 Solution: m m B mx -3 g, 5.x - m, θ a. The fee body diagam of point chage : T cosθ e θ T mg θ T sinθ Since the chages ae in euilibium, thus the point chage also in euilibium then x e T sinθ ( mg T cosθ ( ( By dividing e. ( with e. (, e (3 because tanθ B e and 4πε then e. (3 becomes S7 7 4 mg and y 4πε B tanθ mg 4. x C

8 b. By applying Coulomb s law euation : B e 4πε e 4πε. 7 N e xample 5 : (execise Two point chages ae placed on the x-axis as follows : Chage +4. nc is located at x. m, chage +5. nc is at x -.3 m. ind the magnitude and diection of the total electic foce exeted by these two chages on a negative point chage 3-6. nc that is placed at the oigin. (Young & feedman,pg.89,no.. (Given ε 8.85 x - C N - m - ns. :.4 µn to the ight S7 5 xample 6 : (execise ou identical point chages ( +. µc ae located on the cones of a ectangle as shown in figue below. + + l + + The dimension of the ectangle ae l 6. cm and w 5. cm. Calculate the magnitude and diection of the esultant electic foce exeted on the chage at the lowe left cone by the othe thee chages. (Seway & Jewett, pg. 735, no. 57 (Given ε 8.85 x - C N - m - ns. : 4.9 N at 63 w S7 6

9 3.. Relation of electic foce, e and centipetal foce, c Conside an electon(-ve obiting the nucleus (+ve of an atom in cicula obit of adius, at tangetial (linea speed, v as shown in v figue below. electon nucleus Since e p e thus The electic foce between electon and nucleus contibute the net foce (centipetal foce. ke whee m v e e c ke p mev -3 m : electon mass 9.x kg -9 e : electon chage.6x C k : Coulomb(electostatic constant S Compaison between Newton s Law of Gavitation and Coulomb s Law. Newton s s law of Gavitation Only attactive foce Coulomb s s law ttactive o epulsive foce oce due to mass inteaction The foce is a long-ange foces. The euation of the gavitational foce : Gmm g oce due to chage inteaction The foce is a shot-ange foce. The euation of the electic foce : k e S7 8

10 3.3 lectic ield Definition is defined as a egion of space aound isolated chage whee an electic foce is expeienced if a positive test chage placed in the egion. lectic field aound chages can be epesented by dawing a seies of lines. These lines ae called electic field lines (lines of foce. The diection of electic field is tangent to the electic field line at each point. igues below show the electic field pattens aound the chage. a. Single positive chage b. Single negative chage ield diection + - (the lines point adially outwad (the lines point adially inwad fom the chage towad the chage S7 9 c. Two eual point chages of opposite sign, + and - ield diection + - (the lines ae cuved and they ae diected fom the positive chage to the negative chage. d. Two eual positive chages, + and + ield diection + X + (point X is neutal point is defined as a point (egion whee the total electic foce is zeo. It lies along the vetical dash line. S7

11 e. Two opposite uneual chages, + and ield diection (note that twice as many lines leave + as thee ae lines enteing, numbe of lines is popotional to magnitude of chage. f. Two opposite chaged paallel metal plates The electic field lines ae pependicula to the suface of the metal plates. The lines go diectly fom positive plate to the negative plate. The field lines ae paallel and eually spaced in the cental egion fa fom the edges but finge outwad nea the edges. Thus, in the cental egion, the electic field has the same magnitude at all points. The finging of the field nea the edges can be ignoed because the sepaation of the plates is small compaed to thei size. S7 Simulation g. Two eual negative chages, - and - (execise. - - h. Two uneual negative chages, - and - (execise. - - The popeties of electic field lines: The field lines indicate the diection of the electic field (the field points in the diection tangent to the field line at any point. The lines ae dawn so that the magnitude of electic field is popotional to the numbe of lines cossing unit aea pependicula to the lines. The close the lines, the stonge the field. lectic field lines stat on positive chages and end on negative chages, and the numbe stating o ending is popotional to the magnitude of the chage. The field lines neve coss because the electic field don t have two value at the same point. S7

12 3.4 lectic ield Stength (intensity, The electic field stength at a point, Definition is defined as the electic (electostatic foce pe unit positive chage that acts at that point in the same diection as the foce. Mathematically, whee It is a vecto uantity. The units of electic field stength is N C - o m -. Since k, then the euation above can be witten as k k o 4 πε :magnitude of isolated point chage : distance between the point and isolated point chage whee S7 3 : magnitude of the electic field stength : magnitude of the electic foce : magnitude of test chage Note : The diection of the electic field stength, depends on the sign of isolated point chage. The diection of the electic foce, depends on the sign of isolated point chage and test chage. o example positive isolated point chage. a. positive test chage b. negative test chage ( + ve ( ve S7 4

13 negative isolated point chage. a. positive test chage b. negative test chage ( + ve ( ve In the calculation of magnitude, substitute the magnitude of the chage only. Simulation S7 5 xample 7 : Two point chages, C and -4 C, ae placed cm and 3 cm fom the point espectively as shown in figue below. + - ind cm 3 cm a. the magnitude and diection of the electic field intensity at point. b. the total electic foce exeted on -4 C if it is placed at point. (Given Coulomb s constant, k 9. x 9 N m C - Solution: C, 4 C, 4 C, x - m, 3x - m + - cm 3 cm a. By applying the euation of electic field stength, the magnitude of at point. Due to : k ( 9. x ( 9 ( x S7 3. 5x N C Diection : to the ight ( 6

14 Due to : k ( 9. x ( 4 9 ( 3x 3 4x N C Diection : to the ight ( theefoe the electic field stength at point due to the chages is given by x + 4x x N C b. om the definition of the electic field stength, thus the total electic foce exeted on is given by 3 ( 4( 6. 5x 4. 5x N Diection : to the left ( 3 Diection : to the ight ( S7 7 xample 8 : (execise ind the magnitude of the electic field at point P due to the fou point chages as shown in the figue below if nc and d cm. (Given ε 8.85 x - C N - m - (HRW. pg. 54. ns. : zeo. xample 9 : (execise ind the magnitude and diection of the electic field at the cente of the suae in figue below if.x -8 C and a 5cm. (Given ε 8.85 x - C N - m - (HRW. pg ns. :.x 5 N C -, upwads. S7 8

15 3.5 Motion of Chaged Paticles in a Unifom lectic ield Conside a stationay paticle of chage and mass m is placed in a unifom electic field, the electic foce e exeted on the chage is given by e Since only electic foce exeted on the paticle, thus this foce contibutes the net foce, and causes the paticle to acceleate. ccoding to Newton s second law, then the magnitude of the acceleation of the paticle is e ma ma a m Because the electic field is unifom (constant in magnitude and diection then the acceleation of the paticle is constant. If the paticle has a positive chage, its acceleation is in the diection of the electic field (figue 3.5a. If the paticle has a negative chage (electon, its acceleation is in the diection opposite the electic field (figue 3.5b. S7 9 a e a e ig.3.5a ig.3.5b Conside an electon (e with mass, m e entes a unifom electic field, pependiculaly with velocity v, the downwad electic foce will cause the electon to move along a paabolic path towads lowe plate (figue 3.5c. x v y v ig.3.5c Simulation S7 3

16 Theefoe the acceleation of the electon is given by e a m e The negative sign indicates the diection of the acceleation is in y axis (downwad. om the figue 3.5c, the path is simila to the motion of a ball pojected hoizontally above the gound. The component of its velocity at time t ae given by. x-component : v x v constant y-component : vy v y + ayt and v y v e t y me The position of the electon at time t is x vt S7 3 ˆj y v yt a t e y t m e y 3.6 lectic lux, Φ lectic flux of a unifom electic field, Definition is defined as the scala poduct between the electic field stength, with the vecto of the suface aea, a,. Mathematically, Φ o Φ cosθ whee It is a scala uantity. The unit of electic flux is N m C -. : magnitude of the electic field stength :magnitude of the vecto of suface aea θ :angle between and Conside a unifom electic field passing though a suface aea as shown in figues 3.6a and 3.6b. aea, om the fig. 3.6a, θ, thus o Φ cos Φ S7 3 ig. 3.6a

17 aea, θ om the fig. 3.6b, the angle between and is θ, thus Φ cosθ Note that the diection of vecto is always pependicula (nomal to the suface aea,. ig. 3.6b The electic flux is popotional to the numbe of field lines passing though the aea. Let us conside the moe geneal case, when the electic field is not unifom and the suface is not flat as shown in figue 3.6c. We divide up the chosen suface into n small elements of suface whose aeas ae,, n. ig. 3.6c i We choose the division so that each of i is small enough that it can consideed flat. the electic field can be consideed unifom ove this tiny aea. S7 33 Then the electic flux though the entie suface is appoximately n Φ i i i If i, the sum becomes an integal ove entie suface and and the elation becomes mathematically exact : Φ In many cases, we deal with the flux though a closed suface and the net flux though the suface is given by Φ d d whee the integal sign is witten to indicate that the integal is ove the value of on an enclosing suface. Note :The diection of vecto d is always point outwad fom the enclosed suface as shown in figue 3.6d. o Φ dcosθ S7 ig. 3.6d 34

18 3.7 Gauss s Law States The total electic flux though an enclosed suface is popotional to the algebaic sum of the electic chages within the suface. Mathematically, enc Φ d ε whee : magnitude of the electic field stength d:magnitude of the vecto of suface aea :algebaicsum of the electic chages in enclosed suface : pemittivity of fee space enc ε 3.7. uivalent of Gauss s law and Coulomb s law igue 3.7a shows a positive point chage, aound which we have dawn a concentic spheical Gaussian suface of adius. Gaussian om the Gauss s law : suface enc ε enc Φ dcosθ S7 o ε 35 ig. 3.7a d Φ and d θ Φ enc and ε Since the electic field stength, is consideed unifom hence Φ d and ε d 4π Φ ( 4π ε and k 4πε 4πε k Because then k d enc (suface aea of the Gaussian suface xecise: Deived Gauss s s law by using Coulomb s s law. Coulomb s s Law S7 36

19 3.7. lectic field of a Unifomly Chaged Insulating Sphee Conside an insulating solid sphee of adius R has a unifom volume chage density ρ and caies a total positive chage as shown in figue 3.7b and 3.7c. +++ Gaussian suface R R ig. 3.7b To find the magnitude of electic field inside the sphee, a spheical gaussian suface smalle than the sphee is dawn (figue 3.7b. This gaussian suface having the adius < R. Denote the volume of this small sphee is and the chage inside is in ( in < The volume chage density ρ of a insulating solid sphee is given by ρ constant 4 πr 3 3 S7 37 ig. 3.7c Gaussian suface Theefoe the chage inside the smalle gaussian suface in is πr in ρ' π 4 3 R The magnitude of the electic field is constant and nomal to the suface at each point eveywhee on the gaussian suface both conditions. By applying Gauss s law, in Φ d and ε d 4π 3 d ( 4π 3 εr then the magnitude of the electic field inside the sphee: 4πεR Inside 3 (<R 3 3 S7 38

20 To find the magnitude of electic field outside the sphee, a spheical gaussian suface bigge than the sphee is dawn (figue 3.7c. This gaussian suface having the adius > R. Denote the chage outside is out and out By applying Gauss s law, Φ d ε d ( 4π then the magnitude of the electic field outside the sphee: Hence the gaph of against fo a unifomly chaged insulating sphee can be shown in figue 3.7d. out ε Outside (>R 4πε S7 39 4πε R R R ig. 3.7d lectic field of a Chaged Conducting Sphee Conside a solid conducting sphee of adius R caies a net (total positive chage as shown in figue 3.7e. om the figue 3.7e, the positive chage esides on its suface only R It is because the conducting sphee in electostatic euilibium (no net motion of chage within a conducto. Gaussian suface S7 4 ig. 3.7e

21 Then the magnitude of the electic field inside the conducting sphee is given by Inside (<R To find the magnitude of electic field outside the sphee, a spheical gaussian suface bigge than the sphee is dawn (figue 3.7e. o this choice, both conditions ae satisfied, as they wee fo the insulating sphee in subtopic This gaussian suface having the adius > R and the chage outside is out. om the Gauss s law, Φ d ε d ( 4π then the magnitude of the electic field outside the sphee: out ε Outside (>R 4πε S7 4 Hence the gaph of against fo a chaged conducting sphee can be shown in figue 3.7f R πε R R ig. 3.7f S7 4

22 3.7.4 lectic field of a Line Chage. Conside an infinitely long chaged thin wie whee the electic chage is distibuted unifomly on the wie. The wie has a line of positive chage of infinite length and constant chage pe unit length λ as shown in figue 3.7g. d Gaussian suface d Φ l wie ig. 3.7g ig. 3.7h The symmety of the chage distibution euies that be pependicula to the line chage and diected outwad as shown in figue 3.7h. To find the magnitude of the electic field at distance fom the wie, a cylindical gaussian suface is dawn (figue 3.7g. S7 43 The gaussian suface having the length l and adius. o this choice, both conditions ae satisfied, as they wee fo the insulating sphee in subtopic The chage inside the cylindical gaussian suface is given by in λl By using the Gauss s law, in Φ d ε λl d ( πl ε then the magnitude of the electic field at distance fom the wie: λ πε The electic flux at the end of the cylindical gaussian suface is zeo because the angle between and d is 9 (figue 3.7g.Theefoe the electic flux is given by Φ o d πl k 4πε S7 44 and λ k whee o d dcosθ dcos9

23 3.7.5 lectic field of an infinite Plane Sheet of Chage. Conside an infinite sheet with thin and flat suface on which thee is a unifom positive chage pe unit aea,σ as shown in figue 3.7i. om the figue 3.7i, the diection of is pependicula to the plane and d ig. 3.7i ea, d Gaussian suface have the same magnitude at all points euidistant fom the plane. To find the magnitude of the electic field due to infinite plane, a small cylinde gaussian suface is dawn (figue 3.7i. Both ends of gaussian suface have an aea and ae euidistant fom the plane. o the cuved suface, the angle between and d is 9 thus the electic flux though the cuved suface is zeo. o the flat ends of the cylinde, both conditions ae satisfied thus the electic flux though each end is Φ d d and d Φ S7 45 theefoe the total electic flux though the entie gaussian suface is Φ + The chage inside the gaussian suface is given by in σ By applying the Gauss s law, in Φ d ε σ ε then the magnitude of the electic field due to an infinite plane : σ ε Note: o the conducto plane sheet, the chage esides on its suface and all the electic field lines leave on one side of the suface. Thus the total electic flux is Φ By using the Gauss s law, we get the magnitude of the electic field is σ ε S7 46 Non-conducto plane sheet

24 3.8 lectic Potential, Conside a positive point chage (+ held stationay at O exets a epulsive foce e on a positive test chage (+ at P (figue 3.8a. and B ae two points on the line that passes though O and P. O + + ig. 3.8a P d + The test chage at P is moved by an extenal foce, though a small distance d towads. d is so small that the foce can be consideed to be constant. Thus the wok done dw by the extenal foce is given by o dw dcos and e dw e d k k then dw d Since e S7 47 e B The total wok done W in binging the test chage (+ fom B to is given by dw k d W k W k k whee U If and then the wok done in binging the test chage fom infinity to point (W is k W U o W U 4 πε whee U : electic potential enegy :distance between the point with point chage k : electostatic constant S7 48 o and W U U B k U B

25 lectic potential, of a point in the electic field Definition is defined as the wok done in binging positive test chage fom infinity to that point in the electic field. f o whee W W : wok done : test chage Since W then the euation above can be witten as whee k k k o 4 πε :distance between the point with :point chage : pemittivity of fee space ( ε 8. 85x C N ε m the point chage S7 49 W U lectic potential is a scala uantity. The S.I. unit fo electic potential is the olt ( o J C -. The total electic potential at a point in space is eual to the algebaic sum of the constituent potentials at that point. Note : The theoetical zeo of electic potential of a chage is at infinity. The electic potential enegy of a positively chaged paticle inceases when it moves to a point of highe potential. The electic potential enegy of a negatively chaged paticle inceases when it moves to a point of lowe potential. Since chage can be positive o negative, the electic potential can also be positive o negative. If the value of wok done is negative wok done by the electic foce (system. If the value of wok done is positive wok done by the extenal foce o on the system. In the calculation of, the sign of the chage must be substituted in the euation of. S7 5

26 xample : igue below shows a point at distance m fom the positive point chage, 5C. Calculate the electic potential at point and descibe the meaning of the answe. (Given Coulomb s constant, k 9. x 9 N m C - Solution: 5 C, m By applying the euation of the electic potential at a point, 9 k ( 9. x ( x m 9 J C Meaning : 4.5 x 9 joule of wok is done in binging C positive chage fom infinity to the point. S7 5 xample : Two point chages, +.3 C and -.4 C ae sepaated by a distance of 6 m as shown in figue below m Calculate a. the electic field stength and b. the electic potential at point ( 3 m fom the chage. (Given Coulomb s constant, k 9. x 9 N m C - Solution: +.3 C, -.4 C m 3 m a. By applying the euation of electic field stength, the magnitude of at point. 9 k ( 9. x (. 3 Due to : ( 3 8 3x N C Diection : to the ight ( S7 5

27 Due to : k ( 9. x (. 4 9 ( 3 8 4x N C Diection : to the ight ( theefoe the electic field stength at point due to the chages is given by + 8 3x + 4x 8 7x N C b. By applying the euation of electic potential, the value of at point is + k k + + k x x S Diection : to the ight ( ( xample : Two point chages, + nc and - nc ae sepaated by a distance of 8 cm as shown in figue below. P 6 cm cm Detemine the electic potential at point P( 6 cm fom the chage. (Given Coulomb s constant, k 9. x 9 N m C - Solution: +x -9 C, -x -9 C P x m 6 x m S7 8x m

28 By applying the euation of electic potential, the value of at point P is P P + P k k P + P 7 k + xample 3 : (execise ou point chages ae located at the cones of a suae that is 8. cm on a side. The chages, going in otation aound the suae, ae,, -3 and, whee 4.8 µc as shown in figue below. 8 cm ind the electic potential at the cente of the suae. (Given ε 8.85 x - C N - m - ns. :.53 x 6. 3 S Potential Diffeence Potential diffeence between two points in an electic field, Definition is defined as the wok done in binging a positive test chage fom a point to anothe point in the electic field. om the figue 3.8a, the potential diffeence between point and B, B is given by whee W B B W B B and B B o W B B : wok done in binging positive test chage fom point B to point. : electicpotentialat point :electic potential at point B : test chage S7 56

29 Note : If the positive test chage moving fom point to point B, thus the potential diffeence between this points is given by whee W B B W B B B : wok done in binging positive test chage fom point to point B. : potentialdiffeencebetween point B and point theefoe B B S7 57 xample 4 : Two point chages +.4 nc and -6.5 nc ae. m apat. Point is midway between them, point B is.8 m fom and.6 m fom as shown in figue below..8 m B m.5 m m (Given Coulomb s constant, k 9. x 9 N m C - Solution: +.4x -9 C, -6.5x -9 C,.5 m, B.8 m, B.6 m a. By applying the euation of electic potential, the value of at point is + k k + S ind a. the electic potential at point, b. the electic potential at point B, c. the wok done by the electic field on a chage of.5 nc that tavels fom point B to point. (Young & feedman,pg.9,no.3.

30 b. By applying the euation of electic potential, the value of at point B is B B + B k k B + B B 75 c. Given.5x -9 C The wok done in binging chage, fom point B to point is given by W B B W B 8 WB 8. 5x J xample 5 : test chage +.3x -4 C is 5 cm fom a point chage. wok done of +4 J is euied to ovecome the electostatic foce to bing the test chage to a distance 8 cm fom chage. Calculate : a. the potential diffeence between point 8 cm and 5 cm fom the point chage,. b. the value of chage. S7 59 B ( B c. the magnitude of the electic field stength fo chage at point 5 cm fom the chage. (Given Coulomb s constant, k 9. x 9 N m C - Solution: +.3x -4 C e 5x m 8x m a. Given W B +4J, om the figue above, 5x - m, B 8x - m By applying the euation of potential diffeence, the value of B is W B B B. b. The electic potential at point due to point chage, : 74x 9 k ( 9x ( 5x 8x. 4 B S7 6

31 The electic potential at point B due to point chage, : The potential diffeence between point and B is B 9 k ( 9x 5x ( 8x. B B 4. 74x. 8x. 5x c. By using the euation of electic field stength, thus B. 58x k and 7 C 9. 9x 5 B N C B. 74x 4 S Relation Between and Conside a positive test chage, placed nea a positive point chage,. To move towads by a small displacement (, wok done ( W must be expended as shown in figue 3.8b. + ig. 3.8b The wok done by the extenal foce is given by o and Since W cos W e W then whee S7 6 e e o + e and : potential diffeence : changein displacement(distance : electic field stength e

32 In the limit when appoaches zeo, limit d d The negative sign indicates that the value of electic potential deceases in the diection of electic field. d is known as the electic potential gadient. It can be obtained d fom the gadient of a against gaph. n altenative unit fo electic field stength, is volts pe mete whee N C m The electic field poduced by a pai of flat metal plates, one of which is eathed and the othe is at a potential of is unifom. This can be shown by eually spaced lines of foce in figue 3.8c. S7 63 d + ig.3.8c ig. 3.8d d The against gaph fo pai of flat metal plates can be shown in figue 3.8d. om the figue 3.8d, The gaph is a staight line with negative constant gadient, thus ( ( d o d Unifom d S7 64

33 3.9 uipotential Suface Definition is defined as the locus of points that have the same electic potential. igues 3.9a and 3.9b ae example of the euipotential suface. C B B C ig. 3.9a : a unifom electic field poduced by an infinite sheet of chage ig. 3.9b:a point chage The dashed lines epesent the euipotential suface (line. The euipotential sufaces (lines always pependicula to the electic field lines passing though them. S7 65 om the figues, B C then the wok done to bing a test chage fom B to is given by W ( B B B W B No wok is done in moving a chage along an euipotential suface. xample 6 : (execise t a cetain distance fom a point chage, the magnitude of the electic field is 5 m - and the electic potential is -3. k. Calculate a. the distance to the chage. b. the value of the chage. (Seway & Jewett,pg.788,no.7 (Given ε 8.85 x - C N - m - ns. : 6. m, -. µc S7 66