11.7 Applications of magnetic forces and fields  (Page 5/11)

Four different proton velocities are given. For each case, determine the magnetic force on the proton in terms of e, $v_0,$ and $B_0.$

An electron of kinetic energy 2000 eV passes between parallel plates that are 1.0 cm 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.

An alpha-particle $(m=6.64\times {10}^{\mathrm{-27}}\text{kg},$ $q=3.2\times {10}^{\mathrm{-19}}\text{C})$ moving with a velocity $\overrightarrow{v}=(2.0\widehat{i}-4.0\widehat{k})\times {10}^6\text{m/s}$ enters a region where $\overrightarrow{E}=(5.0\widehat{i}-2.0\widehat{j})\times {10}^4\text{V/m}$ and $\overrightarrow{B}=(1.0\widehat{i}+4.0\widehat{k})\times {10}^{\mathrm{-2}}\text{T}.$ What is the initial force on it?

An electron moving with a velocity $\overrightarrow{v}=\left(4.0\widehat{i}+3.0\widehat{j}+2.0\widehat{k}\right)\times {10}^6\text{m/s}$ enters a region where there is a uniform electric field and a uniform magnetic field. The magnetic field is given by $\overrightarrow{B}=\left(1.0\widehat{i}-2.0\widehat{j}+4.0\widehat{k}\right)\times {10}^{\mathrm{-2}}\text{T}.$ If the electron travels through a region without being deflected, what is the electric field?

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 $1.8\times {10}^{\mathrm{-5}}\text{T}$ north and a vertical component of $5.0\times {10}^{\mathrm{-5}}\text{T}$ down. (a) What is the path of the electron? (b) What is the radius of curvature of the path?

Repeat the calculations of the previous problem for a proton with the same kinetic energy.

What magnetic field is required in order to confine a proton moving with a speed of $4.0\times {10}^6\text{m/s}$ to a circular orbit of radius 10 cm?

An electron and a proton move with the same speed in a plane perpendicular to a uniform magnetic field. Compare the radii and periods of their orbits.

A proton and an alpha-particle have the same kinetic energy and both move in a plane perpendicular to a uniform magnetic field. Compare the periods of their orbits.

A singly charged ion takes $2.0\times {10}^{\mathrm{-3}}\text{s}$ to complete eight revolutions in a uniform magnetic field of magnitude $2.0\times {10}^{\mathrm{-2}}\text{T}.$ What is the mass of the ion?

A particle moving downward at a speed of $6.0\times {10}^6\text{m/s}$ enters a uniform magnetic field that is horizontal and directed from east to west. (a) If the particle is deflected initially to the north in a circular arc, is its charge positive or negative? (b) If B = 0.25 T and the charge-to-mass ratio ( q/m ) of the particle is $4.0\times {10}^7\text{C/kg},$ what is the radius of the path? (c) What is the speed of the particle after it has moved in the field for $1.0\times {10}^{\mathrm{-5}}\text{s}?$ for 2.0 s?

A proton, deuteron, and an alpha-particle are all accelerated through the same potential difference. They then enter the same magnetic field, moving perpendicular to it. Compute the ratios of the radii of their circular paths. Assume that $m_d=2m_p$ and $m_{\alpha }=4m_p.$

A singly charged ion is moving in a uniform magnetic field of $7.5\times {10}^{\mathrm{-2}}\text{T}$ completes 10 revolutions in $3.47\times {10}^{\mathrm{-4}}\text{s}.$ Identify the ion.

Two particles have the same linear momentum, but particle A has four times the charge of particle B. If both particles move in a plane perpendicular to a uniform magnetic field, what is the ratio $R_A\text{/}{R}_B$ of the radii of their circular orbits?