How to Calculate Time for One Revolution of an Ion in a Magnetic Field?

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Homework Help Overview

The problem involves calculating the time it takes for an ion to complete one revolution in a magnetic field, given its charge-to-mass ratio, the magnetic field strength, and the radius of its circular path. The subject area relates to electromagnetism and circular motion.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to find the time for one revolution after calculating the speed of the ion. They question whether to use the circumference for the distance traveled. Some participants clarify that the distance for one revolution is indeed the circumference of the circle.

Discussion Status

The discussion is ongoing, with participants exploring the relationship between the radius, speed, and distance traveled. One participant has provided a calculation for speed and distance but has been questioned about a potential error in the radius used in their calculations. There is no explicit consensus yet on the correctness of the calculations presented.

Contextual Notes

There is a noted discrepancy regarding the radius used in calculations, as the original poster stated a radius of 0.24 m, while another participant referenced 0.42 m in their calculations. This inconsistency may affect the results being discussed.

Invisible101
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Hi, I need help with this question:

An ion with a charge-to-mass ratio of 1.10 x 10^4 C/kg travels perpendicular to a magnetic field (B = 9.10 x 10^-1 T) in a circular path (R = 0.240 m). How long does it take the ion to travel one revolution?

I've found the speed that it travels...then what? How would I find the distance that it travelled? Do I use the circumference? :confused:

I've decided...instead of posting a thread everytime I need help, I'm just going to have one thread and this is where I'll post my questions.
 
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If the ion travels in a circular path then the distance it travels in one revolution must be the circumference of the circle.
 
This is what I did:

q/m = vB┴r
(1.10 x 10^4 C/kg)(9.10 x 10^-1 T)(0.420 m) = v
v = 2402.4 m/s

C = (pie)d (I don't know how to make the symbol)
C = (pie)(0.480 m)
C = 1.507...m

t = d/ = 1.507...m/2402.4 m/s = 6.28 x 10^-4 s

Is this right?
 
I think you switched digits in R. You stated originally that R = 0.24 m but you seem to be using R = 0.42 in your calculation.
 

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