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Julianna Gibson
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1 Emple 1: A positie chge with elocit is moing though unifom mgnetic field s shown in the figues below. Use the ight-hnd ule to detemine the diection of the mgnetic foce on the chge. Emple 1 ˆ i = ˆ ˆ i = ˆ ˆ = ˆ i ˆ = ˆ i ˆ ˆ i = ˆ i ˆ = ˆ i ˆ i = = ˆ ˆ = ˆ i ˆ F M = q ˆ i F M = q ˆ i F M = q ˆ F M = q ˆ j ˆ j z o out F M = q ˆ i ˆ i F M = q ˆ i ˆ i ˆ i F M = q ˆ F M = q ˆ z o in 1 Emple 1 F M = q z ˆ F M = q z ˆ F M = q z ˆ i o left F M = q F M F M = q ˆ i z ˆ F M = q z ˆ i ˆ F M = q z z ˆ z ˆ i F M = q z ˆ i q z Emple : A negtie chge with elocit is moing though unifom mgnetic field s shown in the figues below. Use the ight-hnd ule to detemine the diection of the mgnetic foce on the chge. Qudnt to nd 3 4 Emple F M = q Emple F M = q F M = q ˆ z F M = q z ˆ F M = q z ˆ i F M = q z ˆ i o left F M = q z ˆ ˆ i F M = q z ˆ ˆ i F M = q z ˆ j F M = q z o up F M = q F M = q F M = q F M = No foce F M = q ˆ i F M = q z ˆ i z ˆ ˆ z ˆ j z ˆ i F M = q z ˆ i q z F M = q z ˆ Qudnt F M to nd 5 6

2 Emple 3: A bem of potons moes t m/s though unifom mgnetic field with mgnitude T tht is diected long the positie z-is. The elocit of ech poton lies in the z-plne t n ngle of 3 to the z-is. Find the foce on the poton. 7 Emple 3 q = C, = 31 5 m z - plne 3 wt z - is s = Tˆ, F M =? = ˆ i z ˆ = sin ˆ i cos ˆ = 3 z F M = q F M = q sin ˆ i cos ˆ F M = q sin F M = q sin ˆ ˆ i ˆ cos ˆ ˆ ˆ j cos F M = q sin ˆ j 31 5 m F M = C F M = N ˆ j s sin3 T o in F M = q = qsin F M = C 31 5 m F M = N Tsin3 s 8 Emple 4: q A pticle with chge of e nd mss of g entes mgnitude field with mgnitude of 4 T s shown in the figue boe. The speed of the pticle is m/s. Dw the pth of the pticle s it moes though the field. b. Find the dius of the pth. 9 Emple 4 q = C, m = 31 7 g, = m s ˆ i, = 4 T ˆ q. th of pticle F M = q = qˆ i ˆ = q ˆ i ˆ = q The initil foce is upwds nd the pticle continues in cicul pth. b. =? F M = q = m = m = m 31 7 g m q = s = m C 4 T 1 Emple 5:!V = V - - -e - - An electon cceletes fom est though potentil diffeence of V nd then entes mgnetic field with stength of.5 T.. b. c. Wht is the speed of the electon just befoe it entes the mgnetic field? Wht is the foce on the electon s it moes though the field? Descibe the pth of the electon s it moes though the field. 11 Emple 5 q = C, m = g, V = V, =.5 Tˆ!V = V F M = q - F M = eˆ i ˆ - F -e M = e ˆ i ˆ - F M = eˆ j F M = e -. =? b. F M =? K = U = qv F M = q = K K 1 = qv F M = qsin = q 1 m = qv F M = m m.5 T s s qv = C V F M = N m g c. Descible pth = m Cicul pth upwd. 1 s

3 Emple 6: A stight hoizontl wie cies cuent of 5 A fom west to est in egion whee thee is hoizontl mgnetic field towd the nothest with mgnitude of 1. T nd ngle 45. Find the mgnitude nd diection of the foce on 1 m section of the wie. Emple 6 = 5 A, l = 1 m, = 1. T45, F =? F = d l fo unifom - fields F = l F = lˆ i ˆ i F = l ˆ i ˆ i ˆ i F = l ˆ F = l ˆ = l sin ˆ F = 5 A 1 m 1. T sin45 ˆ F = 4.4 Nˆ lso F = l = lsin F = 5 A 1 m 1. T sin45 13 F F = 4.4 N 14 Emple 7:! L A conducto with stight segment of length L pependicul to the -plne, followed b semicicle section of dius, nd finll stight segment with length L pllel to the - is cies cuent in mgnetic field diected in the positie z diection. Find the totl mgnetic foce on the conducto. 15 Emple 7 df = d l d l = d ˆ l nd = ˆ ˆ l = cos ˆ i sin ˆ j ˆ l = sinˆ i cos d l d l = d sinˆ i cos ˆ df = d sinˆ i cos df df = d sinˆ i ˆ d cos ˆ 16 Emple 7 df = d sinˆ i ˆ d cos ˆ Emple 7 df = sind ˆ i ˆ df = sind cosd ˆ cosd ˆ i F = sind cosd ˆ i F = cos ] sin ˆ i ] F = cos cos F = 11 F = sin sin ˆ i ˆ i ˆ i = 17 L d F d l F = Thee is onl - componet due to smmet. The foce on the stight section of length L is : F = L = Lˆ i ˆ = L ˆ i ˆ The totl foce on the wie is : F = L ˆ j = L d l df 18

4 Emple 7 Emple 7 d F = d l df = dlsin = dlsin9 = dl = d df = dfcos = dcos = cosd df = dfsin = dsin = sind d df l df df 19 df = cosd F = cosd F = sin] F = sin sin F = df = sind F = sind F = cos] d df l df df F = cos cos F = Emple 8: Emple 8 =.5 m = 5 A = 1. T =.5 m = 5 A =.5 m, N = 3 tuns, = 5 A, = 1. T, =? = 1. T A cicul coil.5 m in dius, with 3 tuns of wie, lies in hoizontl plne. t cies cuent of 5 A in the counteclocwise sense when iewed fom boe. The coil is in unifom mgnetic field diected towd the ight, with mgnitude 1. T. Find the toque on the coil. = NAsin = 3 5 A 1. T.5 m sin9 = 1.41 N m 1 Emple 9: q 1.3 m 1.4 m q A pi of point chges, q 1 = 5 µc nd q = -3 µc, e moing s shown boe with speed 1 = m/s nd = m/s. At this instnt find. the mgnetic field poduced t the oigin b. the mgnetic foce tht q 1 eets on q Emple 9 1 = m q s ˆ i 1 = 51 6 C 1 =.3 mˆ j ˆ 1 = 1 =.3 mˆ j 1.3 m = 1 = µ o q 1 1 ˆ T 51-6 C m A* 1 =.3 m m s * ˆ i 1 = T ˆ i = T ˆ 3 4

5 Emple 9 =.4 mˆ i q = 31 6 C = µ o q ˆ ˆ = ˆ i 1 7 T 31-6 C m A* =.4 m = T = m s m ˆ ˆ i = T s * ˆ i Emple 9 Emple 9b o = 1 = Tˆ Tˆ o = Tˆ q =.4 mˆ i.3 mˆ j.3 m.4 m 1 = q ˆ 1 = 1 =.3 mˆ i.3 mˆ j 1.5 m.4 m.3 m =.5 m =.8ˆ i Emple 9b 1 = µ o q 1 1 ˆ 1 1 Emple 1: 1 7 T C m A* 1 = F,1 = 31-6 C m 1 = Tˆ F,1 = q m F,1 = Nˆ i ˆ i.8ˆ i.6 s *.5 m Tˆ s 7 - A stight eticl conducto ling on the - is cies cuent fom = - to =. Find the stength nd diection of the mgnetic field fo point which lies on the -is. 8 Emple 1 d l = d = ˆ i = - ˆ = = ˆ i Emple 1 = µ d ˆ 3 Fom integl tbles: = µ d = C 3 d ˆ 3 1 = µ d l ˆ = µ d l = µ ˆ 3 3 = µ d i µ = ˆ i d 3 d ˆ 3 j ˆ i ˆ 9 = µ 1 ˆ = µ = µ ˆ ˆ 3

6 Emple 1 = µ fo >>, = nd = µ = µ infinitel long wie Emple 1 d l - = µ = d l ˆ = µ d l ˆ sin = µ = µ d 3 d Emple 11: Two long, stight, pllel wies pependicul to the plne, ech c cuent but in opposite diections.. b. 1 3d Wie Wie 1 X d d Find the mgnitude nd diection of the mgnetic field t points 1,, nd 3. Find the mgnitude nd diection of the mgnetic field t n point on the -is to the ight of wie in tems of the -coodinte of the point. d 3 Emple = d Wie Wie 1 X 1 = 4d 1 = 1 1 = µ µ 1 1 = µ 4d µ d 1 = µ 8d µ d 1 = µ 8d Emple 11 1 Wie Wie 1 X = d 1 = d = 1 = µ µ 1 = µ d µ d = µ d Wie Wie 1 X 3 1 = d = 3d 3 = 1 3 = µ 1 3 = µ d µ 3 = µ 3d µ 3d 3 = µ d µ 6d 35 1 Emple 11b Wie Wie 1 X d d 1 = d = d = 1 = µ 1 µ = d µ µ d = µ 1 d 1 d 1 = µ d d d = µ d d = µ d d 36

7 Emple 1: Two long wies pependicul to the -is c cuents of.4 A s shown below. oint 1 is locted t the oigin which is hlfw between the wies nd point is on the -is.3 m below the oigin. Find the mgnitude nd diection of the mgnetic field t points 1 nd m.3 m 37 Emple = =.4 m, 1 = =.4 A, 1 =? = T m.4 A A * 1 =.4 m * 1 = T j o 1 = T 7 ˆ 1 = µ = = 1 38 Emple 1 1 = =.5 m, 1 = =.4 A, =? 1.3 m 1.4 m =.5 m Emple 1 oth cuents out of the pge 1 =? = 1 = 1 = = sin 1 = 1 = = µ 1 7 T m.4 A sin A *.4 m = = T.5 m.5 m* * = Emple 1 oth cuents out of the pge 1 1 =.5 m Emple 13: Two stight, pllel, conducting cbles e 4.5 mm pt nd ech c cuent of 15, A in opposite diections. Find the foce between the cbles. = 1 = 1 = 1 cos 1 = µ o 1 7 T m.4 A 1 cos A *.3 m 1 = = T 1.5 m.5 m* * = 41 4

8 Emple 13 d = 4.5 mm, 1 = = 15, A in opposite diections, F l =? F,1 = 1 l ˆ F,1 = 1 l ˆ j F,1 = 1 l ˆ F,1 = 1 l ˆ i F,1 l = µ 1 d ˆ i d 1 = µ 1 = d = d 1 = µ T m 15, A 15, A A * F 1, = F,1 = = 1, N m m F 1, = l 1 F 1, = lˆ 1 F 1, = l 1 ˆ F 1, = l 1ˆ i F 1, l = µ 1 d ˆ i 43 Mgnetic field t the cente of single loop of cuent cing wie. = µ d 1sin9 = µ = µ d l ˆ A = Asin dl ˆ sin d l = d ˆ l dl = d d l = µ d µ = = µ = µ 44 Emple 14: d l = d ˆ Emple 14 = ˆ i sin cos ˆ z A cicul conducting loop with dius cies cuent. The loop lies in the z-plne t the oigin of the -is. Find the mgnetic field t point tht lies long the -is. z = d l d = cos sin ˆ d l d d l = d ˆ d l = d ˆ Emple 14 We he smmet nd -components cncel nd -components dd. dl = d - = µ = d l ˆ = µ d 1 1 cos Emple 14 = µ = µ d dl ˆ sin9 47 = µ d = µ 3 3 d 48

Emple 14 = µ 3 = µ 3 d Mgnetic Field of Cicul Loop = µ = µ 3 = = µ = µ 3 3 ˆ i on the is of cicul loop 49 5 Emple 15: Use Ampees Lw to deie the mgnetic field. A distnce fom long stight wie cing cuent.

9 Emple 14 = µ 3 = µ 3 d Mgnetic Field of Cicul Loop = µ = µ 3 = = µ = µ 3 3 ˆ i on the is of cicul loop 49 5 Emple 15: Use Ampees Lw to deie the mgnetic field. A distnce fom long stight wie cing cuent. b. At the cente of solenoid with length L with N tuns cing cuent. c. A long clindicl conducto of dius cing unifom cuent. d. A long clindicl conducto of dius cing cuent whose cuent densit J is nonunifom nd ies s J = b, whee b is constnt nd is mesued fom the centl is of the clinde. 51 Emple 15 Long wie cing cuent d l = µ enc dl = µ = µ = µ d l 5 Emple 15b Solenoid of length L with N tuns cing cuent = d l Emple 15c Long clindicl conducto of dius cing unifom cuent d l < d l = µ enc dl = µ enc d l = µ enc = µ n s = µ n n = N numbe of tuns = L totl length = µ JA = µ = µ < 53 54

10 Emple 15c Long clindicl conducto of dius cing unifom cuent Emple 15c Long clindicl conducto of dius cing unifom cuent d l > = µ < = µ > d l = µ enc = µ dl = µ enc 1 = µ = µ > = Emple 15d Long clindicl conducto of dius cing cuent tht ies s J = b J = b enc = J da A = da = d enc = b d = b 3 d enc = b 4 = b 4 = so b = 4 enc = 4 4 < < Emple 15d Long clindicl conducto of dius cing cuent tht ies s J = b d l enc = 4 4 d l = µ enc dl = µ enc = µ 4 4 = µ 3 4 < < Emple 15d Long clindicl conducto of dius cing cuent tht ies s J = b d l enc = > d l = µ enc dl = µ enc = µ = µ Emple 15d Long clindicl conducto of dius cing 3 cuent tht ies s J = b = µ 3 4 < = µ 1 > = µ > = 59 6

(A) 6.32 (B) 9.49 (C) (D) (E) 18.97

(A) 6.32 (B) 9.49 (C) (D) (E) 18.97 Univesity of Bhin Physics 10 Finl Exm Key Fll 004 Deptment of Physics 13/1/005 8:30 10:30 e =1.610 19 C, m e =9.1110 31 Kg, m p =1.6710 7 Kg k=910 9 Nm /C, ε 0 =8.8410 1 C /Nm, µ 0 =4π10 7 T.m/A Pt : 10