19 If a charged particle enters an external magnetic field and it moves in a circular orbit, then what must be true? 1. The particle maintains a constant velocity in the field. The particle maintains a constant speed in the field. Positive work is done by the field on the particle. Negative work is done by the field on the particle.

A charged particle moving through a magnetic field at right angles to the field with a speed of 27.7 m/s experiences a magnetic force of 2.98 10-4 N. Determine the magnetic force on an identical particle when it travels through the same magnetic field with a speed of 5.14 m/s at an angle of 27.2° relative to the magnetic field.N

13 A proton moves perpendicular to a uniform magnetic field B at a speed of 2.10 x 10' m/s and experiences an acceleration of 1.90 × 10 m/s- in the positive x-direction when its velocity is in the positive z-direction. Determine the magnitude and direction of the field. magnitude direction ---Select--- V

173% NASA and the military have long been interested in so-called “rail guns" to launch projectiles and payloads at very high velocities. A schematic of a rail gun is shown below, where there are two parallel rails separated by a distance d and connected to a powerful battery of voltage V, in a constant magnetic field B = Bok pointing out of the page. The projectile / payload can be modeled as a bar of mass m and resistance R which connects the two rails and completes the circuit. Assume the electrical resistance of the rails is negligible, but take there to be a constant force of kinetic friction with magnitude ƒ between the bar and the rails. (a) What is the current in the circuit when the bar is moving with velocity v? Remember to account for both the battery and the induced EMF. (b) What is the net force on the bar when it is moving with velocity v? (c) Using Newton's second law, F = ma, find a differential equation relating and v. (d) Verify that the solution to your differential…