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Learning objectives

By the end of this section, you will be able to:

  • Describe the effects of magnetic fields on moving charges.
  • Use the right-hand rule 1 to determine the velocity of a charge, the direction of the magnetic field, and the direction of magnetic force on a moving charge.
  • Calculate the magnetic force on a moving charge.

The information presented in this section supports the following AP® learning objectives and science practices:

  • 2.D.1.1 The student is able to apply mathematical routines to express the force exerted on a moving charged object by a magnetic field. (S.P. 2.2)
  • 3.C.3.1 The student is able to use right-hand rules to analyze a situation involving a current-carrying conductor and a moving electrically charged object to determine the direction of the magnetic force exerted on the charged object due to the magnetic field created by the current-carrying conductor. (S.P. 1.4)

What is the mechanism by which one magnet exerts a force on another? The answer is related to the fact that all magnetism is caused by current, the flow of charge. Magnetic fields exert forces on moving charges , and so they exert forces on other magnets, all of which have moving charges.

Right hand rule 1

The magnetic force on a moving charge is one of the most fundamental known. Magnetic force is as important as the electrostatic or Coulomb force. Yet the magnetic force is more complex, in both the number of factors that affects it and in its direction, than the relatively simple Coulomb force. The magnitude of the magnetic force     F size 12{F} {} on a charge q size 12{q} {} moving at a speed v size 12{v} {} in a magnetic field of strength B size 12{B} {} is given by

F = qvB sin θ , size 12{F= ital "qvB""sin"θ} {}

where θ size 12{θ} {} is the angle between the directions of v and B . size 12{B} {} This force is often called the Lorentz force    . In fact, this is how we define the magnetic field strength B size 12{B} {} —in terms of the force on a charged particle moving in a magnetic field. The SI unit for magnetic field strength B size 12{B} {} is called the tesla    (T) after the eccentric but brilliant inventor Nikola Tesla (1856–1943). To determine how the tesla relates to other SI units, we solve F = qvB sin θ size 12{F= ital "qvB""sin"θ} {} for B size 12{B} {} .

B = F qv sin θ size 12{B= { {F} over { ital "qv""sin"θ} } } {}

Because sin θ size 12{θ} {} is unitless, the tesla is

1 T = 1 N C m/s = 1 N A m size 12{"1 T"= { {"1 N"} over {C cdot "m/s"} } = { {1" N"} over {A cdot m} } } {}

(note that C/s = A).

Another smaller unit, called the gauss    (G), where 1 G = 10 4 T size 12{1`G="10" rSup { size 8{ - 4} } `T} {} , is sometimes used. The strongest permanent magnets have fields near 2 T; superconducting electromagnets may attain 10 T or more. The Earth’s magnetic field on its surface is only about 5 × 10 5 T size 12{5 times "10" rSup { size 8{ - 5} } `T} {} , or 0.5 G.

The direction of the magnetic force F size 12{F} {} is perpendicular to the plane formed by v size 12{v} {} and B , as determined by the right hand rule 1 (or RHR-1), which is illustrated in [link] . RHR-1 states that, to determine the direction of the magnetic force on a positive moving charge, you point the thumb of the right hand in the direction of v , the fingers in the direction of B , and a perpendicular to the palm points in the direction of F . One way to remember this is that there is one velocity, and so the thumb represents it. There are many field lines, and so the fingers represent them. The force is in the direction you would push with your palm. The force on a negative charge is in exactly the opposite direction to that on a positive charge.

Questions & Answers

Roofs are sometimes pushed off vertically during a tropical cyclone, and buildings sometimes explode outward when hit by a tornado. Use Bernoulli’s principle to explain these phenomena.
Aliraza Reply
Plz answer the question ☝️☝️
what's the basic si unit of acceleration
Explain why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.
Fabian Reply
Insulators (nonmetals) have a higher BE than metals, and it is more difficult for photons to eject electrons from insulators. Discuss how this relates to the free charges in metals that make them good conductors.
Muhammad Reply
Is the photoelectric effect a direct consequence of the wave character of EM radiation or of the particle character of EM radiation? Explain briefly.
Determine the total force and the absolute pressure on the bottom of a swimming pool 28.0m by 8.5m whose uniform depth is 1 .8m.
Henny Reply
how solve this problem?
P(pressure)=density ×depth×acceleration due to gravity Force =P×Area(28.0x8.5)
for the answer to complete, the units need specified why
muqaddas Reply
That's just how the AP grades. Otherwise, you could be talking about m/s when the answer requires m/s^2. They need to know what you are referring to.
Suppose a speck of dust in an electrostatic precipitator has 1.0000×1012 protons in it and has a net charge of –5.00 nC (a very large charge for a small speck). How many electrons does it have?
Alexia Reply
how would I work this problem
how can you have not an integer number of protons? If, on the other hand it supposed to be 1e12, then 1.6e-19C/proton • 1e12 protons=1.6e-7 C is the charge of the protons in the speck, so the difference between this and 5e-9C is made up by electrons
what is angular velocity
Obaapa Reply
angular velocity can be defined as the rate of change in radian over seconds.
Why does earth exert only a tiny downward pull?
Mya Reply
Why is light bright?
Abraham Reply
what is radioactive element
Attah Reply
an 8.0 capacitor is connected by to the terminals of 60Hz whoes rms voltage is 150v. a.find the capacity reactance and rms to the circuit
Aisha Reply
thanks so much. i undersooth well
Valdes Reply
what is physics
Nwafor Reply
is the study of matter in relation to energy
physics can be defined as the natural science that deals with the study of motion through space,time along with its related concepts which are energy and force
a submersible pump is dropped a borehole and hits the level of water at the bottom of the borehole 5 seconds later.determine the level of water in the borehole
Obrian Reply
Practice Key Terms 5

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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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