A velocity selector in a mass spectrometer uses a 0.150 T magnetic field and a 0.31 × 10⁴ V/m electric field. The fields are uniform and perpendicular to one another. Doubly ionized gold ions (Au²⁺) of mass m pass through the velocity selector zone with an initial velocity perpendicular to both electric and magnetic fields. i) Determine the speed of the particles that pass through the velocity selector zone without being deflected by the fields. Then Au²⁺ particles pass through a region of a transverse magnetic field, where they travel in a circular trajectory with a radius of 14.0 cm. ii) Determine the mass of Au²⁺.

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

In your laboratory, you set up an experiment with a mass spectrometer used to separate ionized particles. A single ionized particle of mass 3.27 × 10^-25 kg and with an energy of 1.00 MeV moves in a circle of radius 18.00 cm in a uniform magnetic field. What would be the orbital radius of a doubly ionized particle of mass 1.59 × 10^-25 kg entering the same magnetic field with an energy of 1.00 MeV?

Given an electron moving in a uniform magnetic field of B = 0.75k̂T and an electric field of E = 4000k̂ V/m, the electron initially follows a circular path in the xy-plane with a radius of 2.5 mm. Determine the number of revolutions completed by the electron at a time when it will have a speed of 6.2 × 10⁸ m/s.

A mass spectrometer uses sulfur isotopes of mass numbers 32, 33, and 34 from a meteorite sample. The directions of the electric field between the plates and the magnetic fields are shown below. The marks formed by singly charged ions of each type on a detector film are equally spaced by 0.0017 m. Determine the new spacing on the detector if the ions are doubly charged.

A mass spectrometer has been configured with a magnetic field strength of about 100 mT along with an entrance-exit hole spacing measuring approximately 7.0 cm. What would be the necessary '∆V' acceleration potential differences required for detecting CH₄⁺ ions? The atomic masses are C = 12.000 u, H = 1.0078 u. The electron's missing mass is negligible at this precision level since it's less than 0.001 u. The following constants should be used during calculations: q = 1.6022 × 10^-19 C, and u = 1.6605 × 10^-27 kg.

A segment of a long current-carrying conductor is placed within a uniform 0.340 T magnetic field, pointing directly out of the plane of the page. The conductor makes two right-angle turns and is positioned as shown in the figure. A current of I = 5.00 A flows within the conductor. What are i) the magnitude and ii) the direction of the magnetic force acting on the conductor due to the magnetic field?

The two wires shown below transmit DC current at a potential of 800 kV. What resistance in the circuit will create a 6.00 N repulsive force on a 20.0 m parallel segment of the wires separated by 0.45 m?