Solution: Since the charges have opposite signs, the force is one of attraction. Its magnitude is ( )

Transcription

1 Poblm 1. A C chag is locatd 3. m fom a C chag. Find th lctostatic foc xtd by on chag on th oth. Solution: Sinc th chags hav opposit signs, th foc is on of attaction. Its magnitud is N 9 9 ( C)(.8 10 C ) k qq 1 9 N m F = = C = 3. m Poblm. Two nighboing clls a ionizd (chagd) by x-adiation. (a) If th chag on ach cll is qual to C and th clls a.5 μm apat, what is th foc xtd by ach cll? (b) If th distanc btwn th clls is doubld, what happns to th foc btwn thm? Solution: (a) Th foc is 14 ( C ) kq 9 N m F = = C =.5 10 m N pulsion (b) With two tims lag, is fou tims lag and th foc is ducd to on fouth ofits pvious valu. Poblm 3. An lcton is acclatd by a constant lctic fild of magnitud 300 N/C. (a) Find th acclation of th lcton. (b) Us th quations of motion with constant acclation to find th lcton s spd aft s, assuming it stats fom st. Solution: (a) Th magnitud of th foc on th lcton is F = qe= E, and th acclation is ( C ) ( 300 N C ) F E a= = = = m m kg 13 8 (b) v vi at 0 ( m s )( s) = + = + = m s m s

2 Poblm 4. Two idntical conducting sphs a placd with thi cnts 0.30 m apat. On is givn a chag of 1 x 10 9 C and th oth a chag of C. (a) Find th lctostatic foc xtd by on sph on th oth. (b) Th sphs a connctd by a conducting wi. Aft quilibium has occud, find th lctostatic foc btwn th two. Solution: (a) Th sphically symmtic chag distibutions bhav as if all chag was locatd at th cnts of th sphs. Thfo, th magnitud of th attactiv foc is 9 9 ( 1 10 C)( C ) kq 1 q 9 N m F = = C = 0.30 m N (b) Whn th sphs a connctd by a conducting wi, th nt chag 9 qnt = q1+ q =.0 10 C will divid qually btwn th two idntical sphs. Thus, th foc is now 9 N m.0 10 C nt k q 9 F = = C m o F = N (pulsion)

3 Poblm 5. Calculat th magnitud and diction of th Coulomb foc on ach of th th chags in th following figu. Solution: Th focs a as shown in th sktch at th ight μc F 1 F F 1 F μc -.00 μc F 3 F cm.00 cm ( C)( C ) kqq 1 9 N m F1 = = N - 1 = C m ( C)( C ) kq 1 q3 9 N m F = = N - 13 = C m ( C)( C ) kq q3 9 N m F3 = = N - 3 = C m Th nt foc on th μ C chag is F = F1 F = 4.7 N (to th lft). Th nt foc on th 1.5μ C chag is F1.5 = F1+ F3 = 157 N (to th ight). Th nt foc on th μc chag is F = F+ F3 = 111 N (to th lft).

4 Poblm. Two small mtallic sphs, ach of mass 0.0 g, a suspndd as pndulums by light stings fom a common point as shown in th figu. Th sphs a givn th sam lctic chag, and it is found that th two com to quilibium whn ach sting is at an angl of 5.0 with th vtical. If ach sting is 30.0 cm long, what is th magnitud of th chag on ach sph? Solution: Consid th f-body diagam of on of th sphs givn at th ight. H, T is th tnsion in th sting and F is th pulsiv lctical foc xtd by th oth sph. +y 5.0 T Σ F = 0 Tcos5.0 = mg, o y m g T = cos5.0 F +x Σ F = 0 F = Tsin 5.0 = mgtan 5.0 x mg At quilibium, th distanc spaating th two sphs is = Lsin5.0. Thus, F mgtan 5.0 kq = bcoms ( Lsin5.0 ) = mgtan 5.0 and yilds ( Lsin5.0 ) q= mgtan 5.0 k kg 9.80 m s tan 5.0 = ( m ) sin5.0 = N m C 7. nc

5 Poblm 7. A pic of aluminum foil of mass kg is suspndd by a sting in an lctic fild dictd vtically upwad. If th chag on th foil is 3.00 μc, find th stngth of th fild that will duc th tnsion in th sting to zo. Solution: If th is zo tnsion in th sting, th lctical foc suppots th nti wight of th foil. Thus, F= qe= mg, so ( kg)( 9.80 m s ) mg E = = = q C N C Poblm 8. A poton acclats fom st in a unifom lctic fild of 40 N/C. At som lat tim, its spd is m/s. (a) Find th magnitud of th acclation of th poton. (b) How long dos it tak th poton to ach this spd? (c) How fa has it movd in this intval? (d) What is its kintic ngy at th lat tim? Solution: (a) p ( C) ( 40 N C) F qe a= = = = m m kg m s (b) m s Δv 5 t= = = s= a m s 19. μ s (c) ( ) 10 ( ) vf vi m s 0 Δ x = = = a.1 10 m s 11.8 m 1 1 KEf = m pvf = kg m s = 7 (d) J

6 Poblm 9. In th following figu, dtmin th point (oth than infinity) at which th total lctic fild is zo. Solution: If th sultant fild is zo, th +y contibutions fom th two chags must b in opposit dictions and also hav 1 = d 1.0 m +x qual magnituds. Choos th lin E E 1 q 1 =.5 μc q =.0 μc conncting th chags as th x-axis, with th oigin at th.5 μc chag. Thn, th = 1.0 m + d two contibutions will hav opposit dictions only in th gions x< 0 and x > 1.0 m. Fo th magnituds to b qual, th point must b na th small chag. Thus, th point of zo sultant fild is on th x-axis at x< 0. Rquiing qual magnituds givs Thus, ( 1.0 m d) Solving fo d yilds.5 + = d.0 k q k q = o μc.0 μc = d ( 1.0 m + d). d = 1.8 m, o 1.8 m to th lftofth.5 μc chag Poblm 10. In th Boh thoy of th hydogn atom, an lcton movs in a cicula obit about a poton, wh th adius of th obit is m. (a) Find th lctostatic foc acting on ach paticl. (b) If this foc causs th cntiptal acclation of th lcton, what is th spd of th lcton? k q1 q k Solution: (a) F = = 9 19 ( N m C )( C ) 10 ( m ) = = (b) c F= m a = m v, so ( m )( N ) F v = = = -31 m kg N. 10 m s

7 Poblm 11. A small.00-g plastic ball is suspndd by a 0.0-cm-long sting in a unifom lctic fild, as shown in th figu. If th ball is in quilibium whn th sting maks a 15.0 angl with th vtical as indicatd, what is th nt chag on th ball? Solution: Consid th f-body diagam shown at th ight. T θ y m g Σ Fy = 0 Tcos θ = mg o T = cosθ Σ F = 0 F = Tsinθ = mgtanθ x F x Sinc F = qe, w hav mg qe = m gtanθ, o mgtanθ q= E kg 9.80 m s tan15.0 q= = C = N C 5.5 μ C

8 Poblm 1. Two point chags lik thos in following figu a calld an lctic dipol. Show that th lctic fild at a distant point along th x axis is givn by th xpssion E x = 4k qa/x 3. Solution: As shown in th sktch, th lctic fild at any point on th x-axis consists of two pats, on du to ach of th chags in th dipol. k q k q E= E E = + + q a y a +q x + E E + k q k q ( x+ a) ( xa) 4ax E= = k q = kq ( x a) ( x+ a) x a x+ a x a 4ax Thus, if x >> a, this givs E kq = x 4 4k qa 3 x Poblm 13. A poton movs.00 cm paalll to a unifom lctic fild with E = 00 N/C. (a) How much wok is don by th fild on th poton? (b) What chang occus in th potntial ngy of th poton? (c) Though what potntial diffnc did th poton mov? Solution: (a) Th wok don is cosθ W = F s = qe scosθ, o 19 W = C 00 N C m cos0 = J (b) Th chang in th lctical potntial ngy is Δ PE = W = J (c) Th chang in th lctical potntial is 19 ΔPE J Δ V = = = -19 q C 4.00 V

9 Poblm 14. A potntial diffnc of 90 mv xists btwn th inn and out sufacs of a cll mmban. Th inn sufac is ngativ lativ to th out sufac. How much wok is quid to jct a positiv sodium ion (Na + ) fom th intio of th cll? Solution: Th wok don by th agnt moving th chag out of th cll is input fild W = W = Δ PE =+ q Δ V = C = C 19 3 J J Poblm 15. Th diffnc in potntial btwn th acclating plats of a TV st is about 5 kv. If th distanc btwn ths plats is 1.5 cm, find th magnitud of th unifom lctic fild in this gion. ΔV J C Solution: E = = = d m N C Poblm 1. Suppos an lcton is lasd fom st in a unifom lctic fild whos stngth is V/m. (a) Though what potntial diffnc will it hav passd aft moving 1.00 cm? (b) How fast will th lcton b moving aft it has tavld 1.00 cm? 3 Solution: (a) V Ed ( V m )( m ) Δ = = = 59.0 V 1 (b) mv 0 KE W PE q( V ) =Δ = =Δ = Δ, so ( ΔV ) 1.0 ( C) ( 59.0 J C ) q v = = = m kg m s Poblm 17. (a) Find th potntial 1.00 cm fom a poton. (b) What is th potntial diffnc btwn two points that a 1.00 cm and.00 cm fom a poton? Solution: (a) V kq ( N m C )( C ) = = = m kq kq 1 1 Δ V = V V = = kq (b) 1 ( ) V = ( N m C )( C ) m m = V

10 Poblm 18. Find th potntial at point P fo th ctangula gouping of chags shown in th figu. Solution: Calling q 3 th chag at th con opposit P, q q q = + + = V V1 V V3 k N m C C C = C m m ( 0.00 ) + ( ) m = V Poblm 19. (a) Find th lctic potntial, taking zo at infinity, at th upp-ight con (th con without a chag) of th ctangl in th following figu. (b) Rpat if th.00- μc chag is placd with a chag of.00 μc. Solution: (a) Calling th.00 μ C chag q 3, V kq q q q k i 1 3 = = + + i i N m C C C = C m m ( 0.000) ( ) + m V =.7 10 V (b) Rplacing C by C in pat (a) yilds V = V

11 Poblm 0. (a) How much chag is on ach plat of a 4.00-μF capacito whn it is connctd to a 1.0-V batty? (b) If this sam capacito is connctd to a 1.50-V batty, what chag is stod? = Δ = F 1.0 V = C = 48.0 μ C Solution: (a) Q C( V) = Δ = = =.00 μ C (b) Q C( V) F 1.50 V C Poblm 1. Consid Eath and a cloud lay 800 m abov Eath to b th plats of a paalll-plat capacito. (a) If th cloud lay has an aa of 1.0 km = m, what is th capacitanc? (b) If an lctic fild stngth gat than N/C causs th ai to bak down and conduct chag (lightning), what is th maximum chag th cloud can hold? A ( m 1 C ) 8 Solution: (a) C = 0 = = N m d F 800 m (b) Q = C( Δ V) = C( E d) max max max 8 ( F)( N C ) ( 800 m ) = = 7 C Poblm. Th potntial diffnc btwn a pai of oppositly chagd paalll plats is 400 V. (a) If th spacing btwn th plats is doubld without alting th chag on th plats, what is th nw potntial diffnc btwn th plats? (b) If th plat spacing is doubld whil th potntial diffnc btwn th plats is kpt constant, what is th atio of th final chag on on of th plats to th oiginal chag? Solution: Fo a paalll plat capacito, Q Q Q d Δ V = = = C Ad A. 0 0 (a) Doubling d whil holding Q and A constant doubls Δ V to 800 V. (b) ( ) 0 A ΔV Q = Thus, doubling d whil holding Δ V and A constant will d cut th chag in half, o Q = Q f i Poblm 3. Th plats of a paalll-plat capacito a spaatd by mm. If th matial btwn th plats is ai, what plat aa is quid to povid a capacitanc of.00 pf? 0 0 A 1 C d F m Solution: C =, so A = = =. 10 m 1 d C N m 5

12 Poblm 4.An ai-filld capacito consists of two paalll plats, ach with an aa of 7.0 cm, spaatd by a distanc of 1.80 mm. If a 0.0-V potntial diffnc is applid to ths plats, calculat (a) th lctic fild btwn th plats, (b) th capacitanc, and (c) th chag on ach plat. ΔV 0.0 V 4 Solution: (a) E = = = V m = 11.1 kv m dictd towad -3 d m th ngativ plat (b) C A d 0 = = ( C N m )( m ) m 1 = F = 3.74 pf (c) Q C( V ) 1 11 = Δ = F 0.0 V = C = 74.7 pc on on plat and 74.7 pc on th oth plat. Poblm 5. A paalll-plat capacito has.00-cm plats that a spaatd by 5.00 mm with ai btwn thm. If a 1.0-V batty is connctd to this capacito, how much ngy dos it sto? Solution: Th capacitanc is C A ( C N m )( m ) 0 13 = = = F -3 d and th stod ngy is m, 1 1 ( W = C Δ V = F ) ( 1.0 V ) = J

13 Poblm. Consid th paalll-plat capacito fomd by Eath and a cloud lay. Assum this capacito will dischag (that is, lightning occus) whn th lctic fild stngth btwn th plats achs N/C. What is th ngy lasd if th capacito dischags compltly duing a lightning stik? Solution: Th capacitanc of this paalll plat capacito is A 1 C 0 ( m ) 8 C = = d = N m F 800 m With an lctic fild stngth of d = 800 m, th potntial diffnc btwn plats is Δ V = Ed= = E = N C and a plat spaation of V m 800 m.4 10 V Thus, th ngy availabl fo las in a lightning stik is 1 1 ( W = C Δ V = F )(.4 10 V ) = J