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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)

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Section summary

  • Magnetic force can supply centripetal force and cause a charged particle to move in a circular path of radius
    r = mv qB , size 12{r= { { ital "mv"} over { ital "qB"} } ,} {}
    where v size 12{v} {} is the component of the velocity perpendicular to B size 12{B} {} for a charged particle with mass m size 12{m} {} and charge q size 12{q} {} .

Conceptual questions

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

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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.

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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?

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

Diagram showing magnetic field lines into the page. Charges are moving from the bottom to the top of the diagram and thus perpendicular to the field lines. Charge a curves to the left. Charge b moves in a straight line from bottom to top. Charge c curves to the right.
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Which of the particles in [link] has the greatest velocity, assuming they have identical charges and masses?

Diagram showing magnetic field lines out of the page. Charge a curves clockwise with a large radius as it moves from the bottom to the top of the diagram. Charge b curves clockwise with a much smaller radius as it moves from lower middle to upper middle of the diagram.
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Which of the particles in [link] has the greatest mass, assuming all have identical charges and velocities?

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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.

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Problems&Exercises

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

A cosmic ray electron moves at 7 . 50 × 10 6 m/s size 12{7 "." "50" times "10" rSup { size 8{6} } `"m/s"} {} perpendicular to the Earth’s magnetic field at an altitude where field strength is 1 . 00 × 10 5 T size 12{1 "." "00" times "10" rSup { size 8{ - 5} } `T} {} . What is the radius of the circular path the electron follows?

4.27 m

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A proton moves at 7 . 50 × 10 7 m/s size 12{7 "." "50" times "10" rSup { size 8{7} } `"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?

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(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 . 00 × 10 7 m/s size 12{5 "." "00" times "10" rSup { size 8{7} } `"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.

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(a) An oxygen-16 ion with a mass of 2 . 66 × 10 26 kg size 12{2 "." "66" times "10" rSup { size 8{ - "26"} } `"kg"} {} travels at 5 . 00 × 10 6 m/s size 12{5 "." "00" times "10" rSup { size 8{6} } `"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.

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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 . 36 × 10 4 m size 12{4 "." "36" times "10" rSup { size 8{ - 4} } " m"} {}

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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 4.00 x 10 6 m/s? (b) What is the voltage between the plates if they are separated by 1.00 cm?

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An electron in a TV CRT moves with a speed of 6 . 00 × 10 7 m/s size 12{6 "." "00" times "10" rSup { size 8{7} } `"m/s"} {} , in a direction perpendicular to the Earth’s field, which has a strength of 5 . 00 × 10 5 T size 12{5 "." "00" times "10" rSup { size 8{ - 5} } `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

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(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?

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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 × 10 26 kg , size 12{2 "." "66" times "10" rSup { size 8{ - "26"} } `"kg"} {} and they are singly charged and travel at 5 . 00 × 10 6 m/s size 12{5 "." "00" times "10" rSup { size 8{6} } `"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

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(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 × 10 25 kg size 12{3 "." "90" times "10" rSup { size 8{ - "25"} } `"kg"} {} and 3 . 95 × 10 25 kg size 12{3 "." "95" times "10" rSup { size 8{ - "25"} } `"kg"} {} , respectively, and they travel at 3 . 00 × 10 5 m/s size 12{3 "." "00" times "10" rSup { size 8{5} } `"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.

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Questions & Answers

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.
Giovani Reply
What is meant by dielectric charge?
It's Reply
what happens to the size of charge if the dielectric is changed?
Brhanu Reply
omega= omega not +alpha t derivation
Provakar Reply
u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
Abrar
do to be peaceful with any body
Brhanu Reply
the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
Saeed Reply
if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
Saeed
define variable velocity
Ali Reply
displacement in easy way.
Mubashir Reply
binding energy per nucleon
Poonam Reply
why God created humanity
Manuel Reply
Because HE needs someone to dominate the earth (Gen. 1:26)
Olorunfemi
why god made humenity
Ali
Is the object in a conductor or an insulator? Justify your answer. whats the answer to this question? pls need help figure is given above
Jun Reply
ok we can say body is electrically neutral ...conductor this quality is given to most metalls who have free electron in orbital d ...but human doesn't have ...so we re made from insulator or dielectric material ... furthermore, the menirals in our body like k, Fe , cu , zn
Abrar
when we face electric shock these elements work as a conductor that's why we got this shock
Abrar
how do i calculate the pressure on the base of a deposit if the deposit is moving with a linear aceleration
ximena Reply
why electromagnetic induction is not used in room heater ?
Gopi Reply
room?
Abrar
What is position?
Amoah Reply
What is law of gravition
sushil Reply

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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