11.7 Applications of magnetic forces and fields  (Page 4/11)

A physicist is designing a cyclotron to accelerate protons to one-tenth the speed of light. The magnetic field will have a strength of 1.5 T. Determine (a) the rotational period of the circulating protons and (b) the maximum radius of the protons’ orbit.

The strengths of the fields in the velocity selector of a Bainbridge mass spectrometer are B = 0.500 T and E = $1.2\times {10}^5\text{V/m},$ and the strength of the magnetic field that separates the ions is $B_o=0.750\text{T}.$ A stream of singly charged Li ions is found to bend in a circular arc of radius 2.32 cm. What is the mass of the Li ions?

The magnetic field in a cyclotron is 1.25 T, and the maximum orbital radius of the circulating protons is 0.40 m. (a) What is the kinetic energy of the protons when they are ejected from the cyclotron? (b) What is this energy in MeV? (c) Through what potential difference would a proton have to be accelerated to acquire this kinetic energy? (d) What is the period of the voltage source used to accelerate the protons? (e) Repeat the calculations for alpha-particles.

A mass spectrometer is being used to separate common oxygen-16 from the much rarer oxygen-18, taken from a sample of old glacial ice. (The relative abundance of these oxygen isotopes is related to climatic temperature at the time the ice was deposited.) The ratio of the masses of these two ions is 16 to 18, the mass of oxygen-16 is $2.66\times {10}^{\mathrm{-26}}\text{kg},$ and they are singly charged and travel at $5.00\times {10}^6\text{m/s}$ in a 1.20-T magnetic field. What is the separation between their paths when they hit a target after traversing a semicircle?

(a) Triply charged uranium-235 and uranium-238 ions are being separated in a mass spectrometer. (The much rarer uranium-235 is used as reactor fuel.) The masses of the ions are $$ $3.90\times {10}^{\mathrm{-25}}\text{kg}$ and $3.95\times {10}^{\mathrm{-25}}\text{kg},$ respectively, and they travel at $3.0\times {10}^5\text{m/s}$ in a 0.250-T field. What is the separation between their paths when they hit a target after traversing a semicircle? (b) Discuss whether this distance between their paths seems to be big enough to be practical in the separation of uranium-235 from uranium-238.

Calculate the magnetic force on a hypothetical particle of charge $1.0\times {10}^{\mathrm{-19}}\text{C}$ moving with a velocity of $6.0\times {10}^4\widehat{i}\text{m/s}$ in a magnetic field of $1.2\widehat{k}\text{T}.$

Repeat the previous problem with a new magnetic field of $(0.4\widehat{i}+1.2\widehat{k})\text{T}.$

An electron is projected into a uniform magnetic field $(0.5\widehat{i}+0.8\widehat{k})\text{T}$ with a velocity of $(3.0\widehat{i}+4.0\widehat{j})\times {10}^6\text{m/s}.$ What is the magnetic force on the electron?

The mass and charge of a water droplet are $1.0\times {10}^{\mathrm{-4}}\text{g}$ and $2.0\times {10}^{\mathrm{-8}}\text{C},$ respectively. If the droplet is given an initial horizontal velocity of $5.0\times {10}^5\widehat{i}\text{m/s},$ what magnetic field will keep it moving in this direction? Why must gravity be considered here?