A permanent magnet has a magnetic dipole moment of 0.190 A m². The magnet is in the presence of an external uniform magnetic field (provided by current-carrying coils) with a magnitude of 0.0800 T, which makes an angle of 19.0° with the orientation of the permanent magnet. (a) What is the magnitude of the torque (in N-m) on the permanent magnet? N.m (b) What is the potential energy (in J) of the system consisting of the permanent magnet and the magnetic field provided by the coils? -0.014 X J

In a particular region, there is a uniform magnetic field with a magnitude of 4.00 T. You take a particle with a charge of +9.00 x 10-6 C, and give it an initial speed of 2.80 x 105 m/s in this field. Assume that, after you release it, the particle is influenced only by the magnetic field. (a) Under these conditions, what is the maximum possible magnitude of the magnetic force experienced by the particle? N (b) Under these conditions, what is the mimimum possible magnitude of the magnetic force experienced by the particle? N (c) If the particle experiences a force with a magnitude that is 30.0% of the magnitude of the maximum force, what is the angle between the particle's velocity and the magnetic field? Use an angle between 0° and 90°.

A bar magnet is attached solidly to a frictionless surface and its length is aligned with the x axis. To the right of the first magnet a short distance away is a second bar magnet with its center placed on the x axis and its length perpendicular to the x axis. The second magnet is free to move. Once placed in position at rest, which best describes the initial motion of the second magnet? The magnet will move toward the fixed magnet. The magnet will not move. The magnet will start to rotate. The magnet will move away from the fixed magnet.

A 15 turn circular wire loop that lies in the xy-plane has a diameter of 0.30 m. A current of 1.5 A travels through the loop such that the current is in the clockwise direction when viewed from above the xy-plane. The loop is in a uniform magnetic field: B = +1.5 T j – 2.0T k. (a) What is the magnetic moment of the current loop? (b) What is the torque exerted on the loop by the magnetic field? (c) What is the potential (orientation) energy of the coil in this magnetic field? As usual, set the potential energy equal to zero when the magnetic moment is perpendicular to the magnetic field. For any vector quantities give the answer in unit-vector notation.

A 7.00 turn circular coil of wire is centered on the origin in the xy-plane. The coil has radius r = 0.150 m and carries a counterclockwise current I = 1.50 A (see the figure below). HINT + B Ꮎ i Apply the expressions for the magnetic moment of a current-carrying loop and the torque on a current-carrying loop. Click the hint button again to remove this hint. (a) Calculate the magnitude (in A m²) of the coil's magnetic moment. . A-m² (b) Find the magnitude (in N m) of the magnetic torque on the coil due to a 0.450 T magnetic field that is directed at an angle = 63.0° from the positive z-direction and has components only in the xz-plane. N⚫m

A permanent magnet has a magnetic dipole moment of 0.160 A · m². The magnet is in the presence of an external uniform magnetic field (provided by current-carrying coils) with a magnitude of 0.0800 T, which makes an angle of 27.0° with the orientation of the permanent magnet. (a) What is the magnitude of the torque (in N• m) on the permanent magnet? N• m (b) What is the potential energy (in J) of the system consisting of the permanent magnet and the magnetic field provided by the coils? J

Suppose that the magnetic dipole moment of Earth is 8.6 x 1025 J/T. (a) If the origin of this magnetism were a magnetized iron sphere at the center of Earth, what would be its radius? (b) What fraction of the volume of Earth would such a sphere occupy? The radius of Earth is 6.37 x 106 m. Assume complete alignment of the dipoles. The density of Earth's inner core is 13 g/cm³. The magnetic dipole moment of an iron atom is 2.1 × 10-23 J/T. Iron has a molar mass of 55.9 g/mol. (Note: Earth's inner core is in fact thought to be in both liquid and solid forms and partly iron, but a permanent magnet as the source of Earth's magnetism has been ruled out by several considerations. For one, the temperature is certainly above the Curie point.) (a) Number i Units (b) Number i Units