Force on Moving Charges & Right Hand Rule Practice Problems

A helium nucleus, composed of two protons and two neutrons, is in motion within a magnetic field B = 1.25 k T. Its velocity is measured at 2.0 × 10⁷ m/s, as shown in the figure below. For every situation outlined, calculate the magnetic force, denoted as F, exerted on this helium nucleus. Please present your solution in terms of its components.

A conducting rod with a mass of m lies in the middle of two frictionless conducting rods. The two rods have a separation x. The uniform magnetic field (of magnitude B) in that region points downward. Should the current in the conducting rod flow in a direction P to Q or Q to P for the rod to roll to the left? 

A group of astrophysicists researching the Van Allen radiation belts surrounding the Earth have identified electromagnetic radiation at a frequency of 60 MHz. They theorize that this radiation is a result of electrons spiraling within the Earth's magnetic field. Determine the strength of the magnetic field in the area where these radiation belts are located.

You are given a cyclotron to distinguish two ions with very similar masses. The magnetic field used has a strength of 2.8000 T. Masses of extra or deficient electrons are assumed negligible when using 5 significant figures. The ions CO₂⁺ and C₃H₈⁺ have a nominal molecular mass of 44. Use the atomic masses of the molecules as 44.010 u and 44.096 u, respectively, to calculate the cyclotron frequencies of the ions. Take 1 u = 1.6605 × 10^-27 kg and e = 1.6022 × 10^-19 C.

Consider a particle accelerator that moves particles along a circular path with a diameter of 72 cm. The accelerator uses a potential difference of 300 V, which reverses its direction after every half cycle. If the accelerator uses a magnetic field of 1.6 T, determine the maximum kinetic energy achieved by an alpha particle moving along this circular trajectory.

Work out the magnitude and direction of the total force experienced by the alpha particle in the image below. Specify direction as a clockwise or counterclockwise angle from the horizontal.