A phosphate molecule PO of mass m = difference |AV| = 4.35 V and enters the mass spectrometer with magnetic field of magnitude |B| = 0.090 T. The particle then follows a semi-circular path shown in the picture before = 1.58 × 10¬25 kg is accelerated across the potential reaching the detector located to the left of its entry point. AV a) Sketch the described situation (you can start with the figure shown in the problem) CLEARLY indicating the direction of the magnetic field inside the mass spectrometer b) Determine the speed of the particle as it enters the region of magnetic field. c) Determine the distance between the entry point of the particle and the detector.

Cosmic rays are high-energy charged particles produced by astronomical objects. Many of the cosmic rays that make their way to the Earth are trapped by the Earths magnetic field and never reach the surface. These trapped cosmic rays are found in the Van Allen beltsdonut-shaped zones over the Earths equator (Fig. 30.34). These cosmic rays are mostly protons with energies of about 30 MeV. The inset in the figure shows a cosmic ray proton as it is about to enter the Earths magnetic field. The cosmic rays velocity is initially perpendicular to the field. Three students discuss what happens to the incoming cosmic ray. Decide which student or students are correct. Figure 30.34 The Van Allen belts are donut-shaped zones of trapped cosmic rays above the Earths surface. Inset: What happens to this cosmic ray as it enters the Earths magnetic field? Shannon: The velocity is perpendicular to the magnetic field, so the cosmic ray just passes through the field and hits the Earths atmosphere. Avi: What you are saying is that the magnetic field exerts no force on the cosmic ray. Actually, it exerts a huge force because the velocity is perpendicular to the magnetic field. The force will be into the page. Cameron: Avi is right. The cosmic ray proton is going to feel a huge magnetic force. Because it is positively charged, it will be pushed upward along the magnetic field lines. Shannon: I never said the force was zero. There is a force, but the force is perpendicular to the magnetic field lines. In this case, thats to the lefttoward the Earth. Avi: The force is perpendicular to the magnetic field, but it also has to be perpendicular to the velocity. Because B and v are both in the plane of the page, the force must be perpendicular to the page.

A superconducting wire of diameter 0.25 cm carries a current of 1000 A. What is the magnetic field just outside the wire?

A positron is an antimatter version of the electron, having exactly the same mass. When a positron and an electron meet, they annihilate, converting all of their mass into energy. (a) Find the energy released, assuming negligible kinetic energy before the annihilation. (b) If this energy is given to a proton in the form of kinetic energy, what is its velocity? (c) If this energy is given to another electron in the form of kinetic energy, what is its velocity?

(a) Calculate the mass of a proton using the charge-to-mass ratio given for it in this chapter and its known charge. (b) How does your result compare with the proton mass given in this chapter?

An electron of kinetic energy 2000 eV passes between parallel plates that are 1.0 an apart and kept at a potential difference of 300 V. What is the strength of the uniform magnetic field B that will allow the electron to travel undeflected through the plates? Assume E and B are perpendicular.

At a particular instant an electron is traveling west to east with a kinetic energy of 10 keV. Earth's magnetic field has a horizontal component of 1.8105 T north and a vertical component of 5.0105 T down. (a) What is the path of the election? (b) What is the radius of curvature of the path?

A proton and a helium nucleus (consisting of two protons and two neutrons) pass through a velocity selector and into a mass spectrometer. The radius of the protons circular path is rp. Find an expression for the radius r of the helium nucleuss path in terms of rp. (You may assume the mass of a proton is roughly equal to the mass of a neutron, and the helium nucleus has the same speed as the proton.)

(a) Calculate the relativistic quantity =11v2/c2for 1.00-TeV protons produced at Fermilab. (b) If such a proton created a +having the same speed, how long would its life be in the laboratory? (c) How far could it travel in this time?

Check Your Understanding What is if v=0.650c?