What is the wire's linear charge density?

[smoics]

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)?

 

[SammyS]

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.