A cyclotron designed to accelerate protons has a magnetic field of magnitude 0.450 T over a region of radius 1.20 m. What are (a) the cyclotron frequency and (b) the maximum speed acquired by the protons?

You are on a spacecraft (Starship) to Mars when Houston informs you that a very large solar storm is coming. You are dead as a doornail if you don’t do something. In order to save your life, and the life of your fellow astronauts, you devise a plan to save yourself by creating a large, square solenoid between you and the sun. The arrangement is depicted below. The incoming solar protons have a mass of mp = 1.673 x 10-23 kg, and maximum energy of Ep = 1.6022 x 10-15 J. The thickness of the solenoid is d=10cm. What needs to be the minimum strength of the magnetic field in order to stop this incoming radiation? (think of what the protons would do once they enter the magnetic field of the magnet)

Two isotopes of carbon, carbon-12 and carbon-13, have masses of 19.93 × 10-27 kg and 21.59 × 10-27 kg, respectively. These two isotopes are singly ionized (+e) and each is given a speed of 5.619 x 105 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.6961 T. Determine the spatial separation between the two isotopes after they have traveled through a half-circle. Use 1.602 × 10-19 C as the elementary charge and give your answer to four significant figures. B (out of screen) Number i 0.00821 Units m

In the figure, a conducting rod of length L= 25.0 cm moves in a magnetic field B → of magnitude 0.490 T directed into the plane of the figure. The rod moves with speed v = 4.00 m/s in the direction shown.  When the charges in the rod are in equilibrium, what is the magnitude E of the electric field within the rod? What is the magnitude Vba of the potential difference between the ends of the rod? What is the magnitude E of the motional emf induced in the rod?