A magnetized sewing needle has a magnetic moment of 9.70 μA ⋅ m2. At its location, the Earth’s magnetic field is 55.0 μT northward at 48.0° below the horizontal. Identify the orientations of the needle that represent (a) the minimum potential energy and (b) the maximum potential energy of the needle–field system. (c) How much work must be done on the system to move the needle from the minimum to the maximum potential energy orientation?

A proton traveling at 17.8° with respect to the direction of a magnetic field of strength 3.75 mT experiences a magnetic force of 6.19 x 10-17 N. Calculate (a) the proton's speed and (b) its kinetic energy in electron-volts. (a) Number i (b) Number i Units Units

A proton traveling at 26.4° with respect to the direction of a magnetic field of strength 2.15 mT experiences a magnetic force of 8.13 × 10-17 N. Calculate (a) the proton's speed and (b) its kinetic energy in electron-volts.

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°.