# 22.5 Force on a moving charge in a magnetic field: examples and  (Page 4/4)

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## Test prep for ap courses

A wire oriented north-south carries current south. The wire is immersed in the Earths magnetic field, which is also oriented north-south (with a horizontal component pointing north). The Earths magnetic field also has a vertical component pointing down. What is the direction of the magnetic force felt by the wire?

1. West
2. East
3. Up
4. North

(b)

## Section summary

• Magnetic force can supply centripetal force and cause a charged particle to move in a circular path of radius
$r=\frac{\text{mv}}{\text{qB}},$
where $v$ is the component of the velocity perpendicular to $B$ for a charged particle with mass $m$ and charge $q$ .

## Conceptual questions

How can the motion of a charged particle be used to distinguish between a magnetic and an electric field?

High-velocity charged particles can damage biological cells and are a component of radiation exposure in a variety of locations ranging from research facilities to natural background. Describe how you could use a magnetic field to shield yourself.

If a cosmic ray proton approaches the Earth from outer space along a line toward the center of the Earth that lies in the plane of the equator, in what direction will it be deflected by the Earth’s magnetic field? What about an electron? A neutron?

What are the signs of the charges on the particles in [link] ?

Which of the particles in [link] has the greatest velocity, assuming they have identical charges and masses?

Which of the particles in [link] has the greatest mass, assuming all have identical charges and velocities?

While operating, a high-precision TV monitor is placed on its side during maintenance. The image on the monitor changes color and blurs slightly. Discuss the possible relation of these effects to the Earth’s magnetic field.

## Problems&Exercises

If you need additional support for these problems, see More Applications of Magnetism .

A cosmic ray electron moves at $7\text{.}\text{50}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ perpendicular to the Earth’s magnetic field at an altitude where field strength is $1\text{.}\text{00}×{\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}T$ . What is the radius of the circular path the electron follows?

4.27 m

A proton moves at $7\text{.}\text{50}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ perpendicular to a magnetic field. The field causes the proton to travel in a circular path of radius 0.800 m. What is the field strength?

(a) Viewers of Star Trek hear of an antimatter drive on the Starship Enterprise . One possibility for such a futuristic energy source is to store antimatter charged particles in a vacuum chamber, circulating in a magnetic field, and then extract them as needed. Antimatter annihilates with normal matter, producing pure energy. What strength magnetic field is needed to hold antiprotons, moving at $5\text{.}\text{00}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ in a circular path 2.00 m in radius? Antiprotons have the same mass as protons but the opposite (negative) charge. (b) Is this field strength obtainable with today’s technology or is it a futuristic possibility?

(a) 0.261 T

(b) This strength is definitely obtainable with today’s technology. Magnetic field strengths of 0.500 T are obtainable with permanent magnets.

(a) An oxygen-16 ion with a mass of $2\text{.}\text{66}×{\text{10}}^{-\text{26}}\phantom{\rule{0.25em}{0ex}}\text{kg}$ travels at $5\text{.}\text{00}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ perpendicular to a 1.20-T magnetic field, which makes it move in a circular arc with a 0.231-m radius. What positive charge is on the ion? (b) What is the ratio of this charge to the charge of an electron? (c) Discuss why the ratio found in (b) should be an integer.

What radius circular path does an electron travel if it moves at the same speed and in the same magnetic field as the proton in [link] ?

$4\text{.}\text{36}×{\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}\text{m}$

A velocity selector in a mass spectrometer uses a 0.100-T magnetic field. (a) What electric field strength is needed to select a speed of $4.00x{10}^{6}$ m/s? (b) What is the voltage between the plates if they are separated by 1.00 cm?

An electron in a TV CRT moves with a speed of $6\text{.}\text{00}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ , in a direction perpendicular to the Earth’s field, which has a strength of $5\text{.}\text{00}×{\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}T$ . (a) What strength electric field must be applied perpendicular to the Earth’s field to make the electron moves in a straight line? (b) If this is done between plates separated by 1.00 cm, what is the voltage applied? (Note that TVs are usually surrounded by a ferromagnetic material to shield against external magnetic fields and avoid the need for such a correction.)

(a) 3.00 kV/m

(b) 30.0 V

(a) At what speed will a proton move in a circular path of the same radius as the electron in [link] ? (b) What would the radius of the path be if the proton had the same speed as the electron? (c) What would the radius be if the proton had the same kinetic energy as the electron? (d) The same momentum?

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 $2\text{.}\text{66}×{\text{10}}^{-\text{26}}\phantom{\rule{0.25em}{0ex}}\text{kg},$ and they are singly charged and travel at $5\text{.}\text{00}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ in a 1.20-T magnetic field. What is the separation between their paths when they hit a target after traversing a semicircle?

0.173 m

(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 $3\text{.}\text{90}×{\text{10}}^{-\text{25}}\phantom{\rule{0.25em}{0ex}}\text{kg}$ and $3\text{.}\text{95}×{\text{10}}^{-\text{25}}\phantom{\rule{0.25em}{0ex}}\text{kg}$ , respectively, and they travel at $3\text{.}\text{00}×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ 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.

Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
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