FSAC 1430 Physique T4 : électricité et magnétisme
Semaine 5 : Magnétostatique (première partie)

APE (apprentissage par exercices)

Chaque étudiant doit préparer, en groupe ou seul, une solution pour les exercices 2, 3, 5 et 8 de la liste ci-dessous. Lors de la séance de tutorat du vendredi, chacun doit pouvoir présenter cette solution et pouvoir répondre aux questions posées par le tuteur en utilisant uniquement cette solution et son document de synthèse personnel (10 pages maximum à ce stade).

Liste

1. Young & Freedman, ed. 10, p. 894, ex. 28-8 (or ed. 11, p. 1055, ex. 27.10)

The magnetic flux through one face of a cube is +0.120 Wb.

  1. What must the total magnetic flux through the other five faces of the cube be?
  2. Why did you not need to know the dimensions of the cube in order to answer part (a)?
  3. Suppose the magnetic flux is due to a permanent magnet like that shown on the figure S05-60. In a sketch, show where the cube in part (a) might be located relative to the magnet.

 

Figure S05-60

2. Young & Freedman, ed. 10, p. 895, ex. 28-11 (or ed. 11, p. 1055, ex. 27.13)

A physic student claims that she has arranged magnets so that the magnetic field within the shaded volume in the figure S05-61 is B = (b - gy2 ) j , where b = 0.300 T and g = 2.00 T/m2 .

  1. Find the net flux of B through the five surfaces that enclose the shaded volume in the figure.
  2. Is the student's claim plausible? Why or why not?

Figure S05-61

3. Young & Freedman, ed. 10, p. 897, ex. 28-37 (or ed. 11, p. 1058, ex. 27.51) +...

The figure S05-62 shows a portion of a silver ribbon with z1 = 11.8 mm and y1 = 0.23 mm, carrying a current of 120 A in the +x-direction. The ribbon lies in a uniform magnetic field, in the y-direction, with magnitude 0.95 T.

Apply the simplified model of the Hall effect presented in Section 28-10 (ed. 10) or in Section 17.9 (ed.11). If there are 5.85 x 1028 free electrons per cubic meter, find

  1. the magnitude of the drift velocity of the electrons in the x-direction;
  2. the magnitude and direction of the electric field in the z-direction due to the Hall effect;
  3. the Hall emf;
  4. Compute the Hall constant and compare it with the experimental value (see page 241 in A. Guissard et R. Prieels, syllabus fsa1402, janvier 1998, tableau 4.1 or page 229 in the paper version).

Figure S05-62

4. Young & Freedman, ed. 10, p. 897, ex. 28-41 (or ed. 11, p. 1056, ex. 27.30)

A particle with initial velocity vo = (5.85 x 103 m/s) j enters a region of uniform electric and magnetic fields. The magnetic field in the region is B = - (1.35 T) k . Calculate the magnitude and direction of the electric field in the region if the particle is to pass through undeflected, for a particle of charge

  1. +0.640 nC;
  2. -0.320 nC.

You can ignore the weight of the particle.

5. Young & Freedman, ed. 10, p. 897, ex. 28-43 (or ed. 11, p. 1059, ex. 27.57)

The magnetic poles of a small cyclotron produce a magnetic field with magnitude 0.85 T. The poles have a radius of 0.40 m, which is the maximum radius of the orbits of the accelerated particles.

  1. What is the maximum energy to which protons ( q = 1.60 x 10-19 C , m = 1.67 x 10-27 kg) can be accelerated by this cyclotron? Give your answer in electron volts and in joules.
  2. What is the time for one revolution of a proton orbiting at this maximum radius?
  3. What would the magnetic field magnitude have to be for the maximum energy to which a proton can be accelerated to be twice that calculated in part (a)?
  4. For B = 0.85 T, what is the maximum energy to which alpha particles ( q = 3.20 x 10-19 C, m = 6.65 x 10-27 kg) can be accelerated by this cyclotron? How does this compare to the maximum energy for protons?

6. Young & Freedman, ed. 10, p. 898, ex. 28-52 (or ed. 11, p. 1059, ex. 27.66)

A conducting bar with mass m and length L slides over horizontal rails that are connected to a voltage source. The voltage source maintains a constant current I in the rails and bar, and a constant, uniform, vertical magnetic field B fills the region between the rails (see Fig. S05-63).

  1. Find the magnitude and direction of the net force on the conducting bar. Ignore friction, air resistance, and electrical resistance.
  2. If the bar has mass m, find the distance d that the bar must move along the rails from rest to attain speed v.
  3. It has been suggested that rails guns based on this principle could accelerate payloads into earth orbit or beyond. Find the distance the bar must travel along the rails if it is to reach the escape speed for the earth (11.2 km/s). Let B = 0.50 T, I = 2.0 x 103 A, m = 25 kg, and L = 50 cm.

Figure S05-63

7. Young & Freedman, ed. 10, p. 900, ex. 28-63 (or ed. 11, p. 1061, ex. 27.81)

It was shown in Section 28-8 (ed. 10) or in Section 27.7 (ed. 11) that the net force on a current loop in a uniform magnetic field is zero. But what if B is not uniform? Figure S05-64 shows a square loop of wire that lies in the xy-plane. The loop has corners at (0, 0), (0, L), (L, 0), (L, L) and carries a constant current I in the clockwise direction. The magnetic field has no x-component but has both y- and z-components; B = (Bo z/L) j + (Bo y/L) k, where Bo is a positive constant.

  1. Sketch the magnetic field lines in the yz-plane.
  2. Find the magnitude and direction of the magnetic force exerted on each of the sides of the loop by integrating equation dF = I dl x B (magnetic force on an infinitesimal wire section).
  3. Find the magnitude and direction of the net magnetic force on the loop.

Figure S05-64

8. Une bobine carrée de 5 cm de côté, comportant 15 spires, est disposée verticalement. Elle est parcourue par un courant de 2.7 A . Cette bobine se trouve dans une région où règne un champ magnétique horizontal de 0.56 T .

a) Donnez une expression littérale du couple exercé sur la bobine en fonction du courant I qui la parcourt, de son nombre n de spires, de la mesure de son côté a, de la norme du champ B et de la position de la bobine (repérée par l'angle q formé par la normale au plan de la bobine avec le champ B.
b) Quelle est l'orientation de la bobine qui rend maximum le couple exercé sur celle-ci et quelle est la valeur du couple maximum ?
c) Pour quelle orientation de la bobine la valeur du couple est-elle égale à 71 % de sa valeur maximum ?

 

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Dernière mise à jour le 14-10-2004