Concepts & Calculations

Note: Each of these problems consists of Concept Questions followed by a related quantitative Problem. The Concept Questions involve little or no mathematics. They focus on the concepts with which the problems deal. Recognizing the concepts is the essential initial step in any problem-solving technique.

| 78 | Concept Questions (a) A charge moves along the +x axis and experiences no magnetic force, although there is a magnetic field. What can you conclude about the direction of the magnetic field? (b) A moving charge experiences the maximum possible magnetic force when moving in a magnetic field. What can you conclude about the angle that the charge’s velocity makes with respect to the magnetic field? Explain your answers.
Problem A particle that has an charge moves with a velocity of magnitude 5.0 × 105 m/s. When the velocity points along the +x axis, the particle experiences no magnetic force, although there is a magnetic field present. The maximum possible magnetic force that the charge could experience has a magnitude of 0.48 N. Find the magnitude and direction of the magnetic field. Note that there are two possible answers for the direction of the field. Make sure that your answers are consistent with your answers to the Concept Questions.

| 79 | Concept Questions A proton is projected perpendicularly into a magnetic field with a certain velocity and follows a circular path. Then an electron is projected perpendicularly into the same magnetic field with the same velocity. (a) Does the electron follow the exact same circular path that the proton followed? (b) To make the electron follow the exact same circular path as the proton, what, if anything, should be done to the direction and the magnitude of the magnetic field? Account for your answer.
Problem A proton is projected perpendicularly into a magnetic field that has a magnitude of 0.50 T. The field is then adjusted so that an electron will follow the exact same circular path when it is projected perpendicularly into the field with the same velocity that the proton had. What is the magnitude of the field used for the electron? Verify that your answer is consistent with your answers to the Concept Questions.

| 80 | Concept Questions Particle 1 and particle 2 carry the same charge q, but particle 1 has a smaller mass than particle 2. These two particles accelerate from rest through the same electric potential difference V and enter the same magnetic field, which has a magnitude B. The particles travel perpendicular to the field on circular paths. Upon entering the field region, which particle, if either, has the greater (a) kinetic energy and (b) speed? Give your reasoning.
Problem The masses of the particles are m1 = 2.3 × 10−8 kg and m2 = 5.9 × 10−8 kg. The radius of the circular path for particle 1 is r1 = 12 cm. What is the radius of the circular path for particle 2?

| 81 | Concept Question The drawing shows a wire composed of three segments, AB, BC, and CD. There is a current I in the wire. There is also a magnetic field that is the same everywhere and points in the direction of the +z axis. Rank the wire segments according to the magnetic force (largest first) that they experience. Justify your ranking.

Problem The lengths of the wire segments are LAB = 1.1 m, LBC = 0.55 m, and LCD = 0.55 m. The current is I = 2.8 A, and the magnitude of the magnetic field is B = 0.26 T. Find the magnitude of the force that acts on each segment. Be sure your answers are consistent with your answer to the Concept Question.

| 82 | Concept Question You have a wire of length L from which to make the square coil of a dc motor. In a given magnetic field a coil of N turns, each with area A, produces more torque when its total effective area of NA is greater rather than smaller. This follows directly from Equation 21.4. Is more torque obtained by using the length of wire to make a single-turn coil or a two-turn coil, or is the torque the same in each case? Explain.
Problem The length of the wire is L = 1.00 m. The current in the coil is I = 1.7 A, and the magnetic field of the motor is 0.34 T. Find the maximum torque when the wire is used to make a single-turn square coil and a two-turn square coil. Verify that your answers are consistent with your answer to the Concept Question.

| 83 | Concept Questions A particle has a charge q and is located at the coordinate origin. An electric field Ex points along the +x axis. A magnetic field also exists, and its components Bx and By point along the +x and +y axis, respectively (see the drawing). Which, if any, of the fields (Ex, Bx, By) exert a force on the particle if it is (a) stationary and (b) moving along the +x axis? Justify your answers. (c) None of the three fields points along the +z axis. If the particle is moving along this axis, does it experience a force due to any of the fields? Provide a reason for your answer.
Problem The electric and magnetic fields in the drawing are, respectively, Ex = +245 N/C, Bx = +1.80 T, and By = +1.40 T, and the charge is . Calculate the force (magnitude and direction) exerted on the particle by each of the three fields when it is (a) stationary, (b) moving along the +x axis at a speed of 375 m/s, and (c) moving along the +z axis at a speed of 375 m/s. Be sure your answers are consistent with those in the Concept Questions.

| 84 | Concept Questions The drawing shows two perpendicular, long, straight wires, both of which lie in the plane of the paper. Each wire carries the same current I. What is the direction of the net magnetic field at (a) point A and (b) point B? (c) Is the magnitude of the net field at point A greater than, less than, or equal to the magnitude of the net field at point B?
Problem The current in each of the wires is I = 5.6 A. Find the magnitudes of the net fields at points A and B. Verify that your answers are consistent with your answers to the Concept Questions.

| 85 | Concept Questions A horizontal wire is hung from the W ceiling of a room by two massless strings. A uniform magnetic field is directed from the ceiling to the floor. When a current exists in the wire, the wire swings upward and makes an angle with respect to the vertical, as the drawing shows. (a) How is the magnitude of the magnetic force related to the magnetic field, the length of the wire, and the current in the wire? (b) What is the direction of the magnetic force? (c) The wire is stationary, so it is in equilibrium. What are the forces that keep it in equilibrium? (d) What must be true about the sum of the forces in the horizontal direction and the sum of the forces in the vertical direction?

Problem The wire has a length of 0.20 m and a mass of 0.080 kg and carries a current of 42 A. The magnitude of the magnetic field is 0.070 T. Find (a) the angle and (b) the tension in each of the two strings.

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