Additional Problems

| 64 | In New England, the horizontal component of the earth’s magnetic field has a magnitude of 1.6 × 10−5 T. An electron is shot vertically straight up from the ground with a speed of 2.1 × 106 m/s. What is the magnitude of the acceleration caused by the magnetic force? Ignore the gravitational force acting on the electron.

| 65 | ssm A long solenoid has 1400 turns per meter of length, and it carries a current of 3.5 A. A small circular coil of wire is placed in side the solenoid with the normal to the coil oriented at an angle of 90.0° with respect to the axis of the solenoid. The coil consists of 50 turns, has an area of 1.2 × 10−3 m2, and carries a current of 0.50 A. Find the torque exerted on the coil.

| 66 | Two charged particles move in the same direction with respect to the same magnetic field. Particle 1 travels three times faster than particle 2. However, each particle experiences a magnetic force of the same magnitude. Find the ratio of the magnitudes of the charges.

| 67 | The maximum torque experienced by a coil in a 0.75-T magnetic field is 8.4 × 10−4 N·m. The coil is circular and consists of only one turn. The current in the coil is 3.7A. What is the length of the wire from which the coil is made?

| 68 | Suppose in Figure 21-28a that I1 = I2 = 25 A and that the separation between the wires is 0.016 m. By applying an external magnetic field (created by a source other than the wires) it is possible to cancel the mutual repulsion of the wires. This external field must point along the vertical direction. (a) Does the external field point up or down? Explain. (b) What is the magnitude of the external field?

| 69 | ssm Due to friction with the air, an airplane has acquired a net charge of 1.70 × 10−5 C. The airplane travels with a speed of 2.80 × 102 m/s at an angle with respect to the earth’s magnetic field, the magnitude of which is 5.00 × 10−5 T. The magnetic force on the airplane has a magnitude of 2.30 × 10−7 N. Find the angle (There are two possible angles.)

| 70 | Two insulated wires, each 2.40 m long, are taped together to form a two-wire unit that is 2.40 m long. One wire carries a current of 7.00 A; the other carries a smaller current I in the opposite direction. The two-wire unit is placed at an angle of 65.0° relative to a magnetic field whose magnitude is 0.360 T. The magnitude of the net magnetic force experienced by the two-wire unit is 3.13 N. What is the current I?

| 71 | A charged particle with a charge-to-mass ratio of travels on a circular path that is perpendicular to a magnetic field whose magnitude is 0.72 T. How much time does it take for the particle to complete one revolution?

| 72 | Two long, straight wires are separated by 0.120 m. The wires carry currents of 8.0 A in opposite directions, as the drawing indicates. Find the magnitude of the net magnetic field at the points labeled (a) A and (b) B.

* | 73 | ssm A particle of charge and mass 3.8 × 10−8 kg is traveling perpendicular to a 1.6-T magnetic field, as the drawing shows. The speed of the particle is 44 m/s. (a) What is the value of the angle , such that the particle’s subsequent path will intersect the y axis at the greatest possible value of y? (b) Determine this value of y.

* | 74 | Two infinitely long, straight wires are parallel and separated by a distance of one meter. They carry currents in the same direction. Wire 1 carries four times the current as wire 2 does. On a line drawn perpendicular to both wires, locate the spot (relative to wire 1) where the net magnetic field is zero. Assume that wire 1 lies to the left of wire 2 and note that there are three regions to consider on this line: to the left of wire 1, between wire 1 and wire 2, and to the right of wire 2.

* | 75 | The drawing shows a parallel plate capacitor that is moving with a speed of 32 m/s through a 3.6-T magnetic field. The velocity is perpendicular to the magnetic field. The electric field within the capacitor has a value of 170 N/C, and each plate has an area of 7.5 × 10−4 m2. What is the magnetic force (magnitude and direction) exerted on the positive plate of the capacitor?

** | 76 | The drawing shows two wires that both carry the same current of I = 85.0 A and are oriented perpendicular to the plane of the paper. The current in one wire is directed out of the paper, while the current in the other is directed into the paper. Find the magnitude and direction of the net magnetic field at point P.

** | 77 | ssm A charge of 4.0 × 10−6 C is placed on a small conducting sphere that is located at the end of a thin insulating rod whose length is 0.20 m. The rod rotates with an angular speed of about an axis that passes perpendicularly through its other end. Find the magnetic moment of the rotating charge. (Hint: The charge travels around a circle in a time equal to the period of the motion.)

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