Proton moving in a magnetic field

• erodger
In summary, when a proton traveling at 1×106 m/s enters a uniform magnetic field of 1.2 T, it will undergo circular motion with a radius of 8.698*10^(-3) m. The time required for the proton to re-emerge into the field-free region is 2.73*10^(-8) seconds. The magnetic field is perpendicular to the initial velocity of the proton, causing it to undergo circular motion. The exact values for the radius and time may vary depending on rounding and precision used in calculations.
erodger

Homework Statement

A proton (mass= 1.67×10-27 kg, charge= 1.6×10-19 C) traveling with speed 1×106 m/s enters a region of space containing a uniform magnetic field of 1.2 T.

The magnetic field is coming out of the screen.

What is the time t required for the proton to re-emerge into the field-free region?

qvB = mv2/R

The Attempt at a Solution

I begin by solving for R using the above equation:

R= (mv)/(qB)

Since the proton moves in and then back out it completes a semi-circle. The distance traveled is then πR as it is half of the circumference of a circle.

The velocity does not change for the entire distance traveled so dividing distance by velocity should give me the time.

This comes out as incorrect though. I am unsure as to what I am doing wrong.

in what direction is the magnetic field pointed relative to the initial velocity of the proton?

Oh sorry, I edited the post. It is coming out of the screen. So it is perpendicular to its motion which means it will create a net force on the proton and cause it to undergo the circular motion.

ah, okay. Well, what did you get for your time?

Well the question involved some steps and one of the steps was to find the radius. It continued to tell me I am wrong. I decided to stop using that and work on it my own using my method and I managed to come up with the correct answer, which just involved me to not round to 2 sig figs but add on more decimal digits. My answer was 2.73*10^(-8). Before I was just putting in 2.7*10^(-8).

Thanks for trying to help.

what did you get for your radius?

huh, actually that's the same time I got.

I got 8.698*10^(-3) for my radius. The computer kept telling me it was incorrect but I managed to get the right answer with this value so I do not know what is wrong...

so the time you got was correct, but the radius is not? Maybe it wants radius in terms of some unit like cm?

No it was asking for metres which is what my answer is in.

interesting... I don't know what to tell you :(

did you try the same thing with what you did with time? Try changing the number of decimal points, or how you round your numbers when you solve for it.Sometimes I have these same problems with online homework things. They usually accept answers within a certain range of the correct answer, but can be really stubborn sometimes :P

1. What is the cause of the proton's motion in a magnetic field?

The proton's motion in a magnetic field is caused by the Lorentz force, which is the result of the interaction between the magnetic field and the proton's positive charge.

2. How does the strength of the magnetic field affect the motion of the proton?

The strength of the magnetic field directly affects the magnitude of the Lorentz force acting on the proton, which in turn determines the curvature and speed of the proton's motion.

3. What is the direction of the proton's motion in a magnetic field?

The direction of the proton's motion is always perpendicular to both the direction of the magnetic field and the direction of the proton's velocity. This is known as the right-hand rule.

4. Can the proton's motion in a magnetic field be controlled?

Yes, the motion of a proton in a magnetic field can be controlled by changing the strength or direction of the magnetic field. This is the principle behind devices such as particle accelerators and MRI machines.

5. What are the practical applications of understanding proton motion in a magnetic field?

Understanding the behavior of protons in a magnetic field has a wide range of practical applications, including medical imaging, particle physics research, and the development of new technologies such as magnetic levitation trains.

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