Finding current of a revolving charged cylinder

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SUMMARY

The discussion centers on calculating the current \( I \cdot n \) for a revolving charged cylinder, specifically in the context of magnetic field equations similar to those for a solenoid. The relevant equation is \( B = \frac{4\pi}{c}(I \cdot n) \). The user initially derived the current as \( \frac{Q\omega}{2\pi} \) but later found that the correct expression should be \( \frac{Q\omega}{L} \), where \( \omega \) is the angular velocity. The confusion arises from the relationship between charge density and the geometry of the cylinder.

PREREQUISITES
  • Understanding of electromagnetism principles, particularly magnetic fields.
  • Familiarity with the equations governing solenoids and their magnetic fields.
  • Knowledge of angular velocity and its relation to linear velocity.
  • Basic concepts of charge density and its calculation in cylindrical geometries.
NEXT STEPS
  • Study the derivation of the magnetic field for a solenoid using \( B = \frac{4\pi}{c}(I \cdot n) \).
  • Learn about charge density calculations in cylindrical coordinates.
  • Explore the relationship between angular velocity \( \omega \) and linear velocity in rotating systems.
  • Investigate the implications of frequency \( f \) in electromagnetic equations, particularly in relation to angular frequency.
USEFUL FOR

Students and professionals in physics, particularly those focusing on electromagnetism, as well as engineers working with rotating charged systems and magnetic field applications.

hangainlover
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Homework Statement


When given Q, ω, and geometry of a cylinder (radius a, length L)
how do you come up with current I*n ? the cylinder is rotating around the axis through the center of the cylinder

this question is essentially the same as finding magnetic field for a solenoid...
I just need to find what is equivalent to I*n in the B equation below...

IT's originally purcell 6.18...but i understand the question except how you come up with I*n (current times the number of turns for solenoid)


Homework Equations


B=(4pi/c)*(I*n)


The Attempt at a Solution


I thought Qω/(2pi) gives you the current..
I found the charge density Q/(2pi*a*L) multiplied it by L (because we want to find the flux of charge through a trip running parallel to the cylinder).
Then, multiplied it by the velocity (ω*a) which gives me Qω(2pi)..
However the answer says it has to be Qω/L ...

here is the solution i found...
http://www.6911norfolk.com/d0lbln/h7bs99/h7bs99-psoln9.pdf
 
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hangainlover said:
I thought Qω/(2pi) gives you the current..

It does.
However the answer says it has to be Qω/L ...

It says the answer has to be Qv/L, where v is frequency. Since ω=2pi*f, this is identical to your formula.
 
But even then, my answer has an extra factor of L...
 

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