What is the wire's linear charge density?

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SUMMARY

The discussion focuses on calculating the linear charge density of a long charged wire around which a proton orbits at a frequency of 1.60 x 10^6 revolutions per second and a radius of 1.60 cm. The equations utilized include F=qE, F=ma, and F=(mw^2)/r. The participant arrives at a linear charge density (λ) of 5.7 x 10^-4 nC/m but identifies this result as incorrect, suspecting a potential error in unit conversion or setup. The correct approach involves ensuring accurate calculations of force and electric field based on the given parameters.

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Homework Statement



A proton orbits a long charged wire, making 1.60 * 10^6 revolutions per second. The radius of the orbit is 1.60 cm. What is the wire's linear charge density?


Homework Equations


F=qE
F=ma
F=(mw^2)/r
F=Eklambda/2r=mw^2/r (the radiuses cancel out)


The Attempt at a Solution


a=w^2/r=((1.60*10^6 rev/s *2pi)^2/.016 m
F=ma m=1/67 *10^-27
E=F/q E=6.59*10^7
F=Eklambda/2r=mw^2/r (the radiuses cancel out)
LAMBDA=5.7*10^-4 nC/m This is incorrect. Where am I going wrong? I have stared at this problem too long and can't figure out what the problem is (it might be some minute conversion issue or something because I think the set up is correct)?
 
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smoics said:

Homework Statement



A proton orbits a long charged wire, making 1.60 * 10^6 revolutions per second. The radius of the orbit is 1.60 cm. What is the wire's linear charge density?


Homework Equations


F=qE
F=ma
F=(mw^2)/r   This should be either F=(mω2)r, or F=(mv2)/r
F=Eklambda/2r=mw^2/r (the radiuses cancel out)


The Attempt at a Solution


a=w^2/r=((1.60*10^6 rev/s *2pi)^2/.016 m
F=ma m=1/67 *10^-27
E=F/q E=6.59*10^7
F=Eklambda/2r=mw^2/r (the radiuses cancel out)
LAMBDA=5.7*10^-4 nC/m This is incorrect. Where am I going wrong? I have stared at this problem too long and can't figure out what the problem is (it might be some minute conversion issue or something because I think the set up is correct)?
See comment in red.
 

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