Charged Particle Motion in a Magnetic Field

In summary, the conversation discusses finding the magnitude of the magnetic field for a proton moving through a vertical magnetic field with a known velocity and acceleration. The correct equation, B = F/(qv), is used to find the magnetic field, but the incorrect mass for the proton is initially used. After realizing the error, the correct mass is used and the correct answer is found.
  • #1
Quantum_Grid
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Homework Statement


A proton is moving through a vertical magnetic field. The (instantaneous) velocity of the proton is 8.5x105m/s horizontally in the north direction. The (instantaneous) acceleration produced by the magnetic force is 2.90x105m/s2 in the west direction. What is the magnitude of the magnetic field?

Homework Equations


Proton Mass = 1.67x10-23 kg
Proton Charge = +e = 1.60x10-19 C
B = F/(qv) (I think!)

The Attempt at a Solution


Okay, this seems like it should be simple, but the online homework keeps saying I am wrong, so obviously I am skipping something here. First, applying Newton's second law, I found the force, F, required of the Magnetic Force to produce the acceleration (F=ma = (1.67x10-23 kg x 2.90x105 m/s2 = 4.843x10-18 N). Then, all I need to do is put this force in the equation for a charged particle in motion in a magnetic field, which I think is B=F/(qv), so I should get, B = (4.843x10-18 N)/[(1.60x10-19 C)(8.5x105m/s), which gives me B = 3.561x10-5 Tesla.

But apparently that is wrong. Am I missing something small, like a number, or do I have the wrong equation?

Thanks!
 
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  • #2
You have the proton mass wrong. The mass is 1.67E-27 kg.
 
  • #3
Ah, thanks! Indeed I do.

And that was off of an equation/constant sheet my professor gave me!

Thanks again, I knew it was something like that.
 

What is a charged particle?

A charged particle is an object that has an electric charge, meaning it has either gained or lost electrons and therefore has a net positive or negative charge. Examples of charged particles include protons, electrons, and ions.

What is a magnetic field?

A magnetic field is a force field created by the movement of electric charge. It is represented by lines of force that extend from a magnet's north pole to its south pole. These lines of force can also be created by moving charged particles, such as in the case of a charged particle moving through a magnetic field.

How does a charged particle move in a magnetic field?

When a charged particle enters a magnetic field, it experiences a force known as the Lorentz force. This force is perpendicular to both the velocity of the particle and the magnetic field, causing the particle to move in a circular or helical path. The direction of the force can be determined using the right-hand rule.

What factors affect the motion of a charged particle in a magnetic field?

The strength of the magnetic field, the velocity of the charged particle, and the charge of the particle all affect its motion in a magnetic field. A stronger magnetic field will result in a greater force on the particle, while a faster-moving particle will also experience a greater force. The direction of the force also depends on the charge of the particle.

What are the applications of charged particle motion in a magnetic field?

The principles of charged particle motion in a magnetic field are used in a variety of applications, including particle accelerators, mass spectrometers, and cathode ray tubes. It is also used in MRI machines to create detailed images of the body's tissues and organs. The behavior of charged particles in Earth's magnetic field is also important for navigation and communication systems that use satellites.

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