Maximum speed of an electron in an ideal solenoid

[efredman]

Homework Statement

A particular ideal solenoid has 1200 turns/m, a radius of 10 cm, and a current of 4.0 A. An electron is fired from the axis of the solenoid in a direction perpendicular to the axis. What is the maximum speed the electron can have if it is not run into the side of the solenoid?


I know the answer is 5.3 ×10^7 m/s but I have no idea how to arrive there... Any help would be great. Thanks.

Homework Equations

u=4pi*10^-7 T m/A

n=N/L

B=u*n*I

The Attempt at a Solution

I just plugged in the values to get B which ended up being .006032T and than used r=(mv)/(qB) to get v... but that didn't seem to work.

 

[gneill]

Don't confuse the radius of the solenoid with the radius of curvature of the electron's trajectory. The electron's trajectory will describe a circle. What's its maximum diameter?