Find Current in a Solenoid Given Magnetic Field and Velocity

[elitepro]

Homework Statement

An electron circles at a speed of 8510 m/s in a
radius of 2.42 cm in a solenoid. The magnetic
field of the solenoid is perpendicular to the
plane of the electron’s path. Find the current in the solenoid if it has
23.3 turns/cm.
Answer in units of mA

Homework Equations

I think you can use B=uIN
I=B/(uN)
u is the universal vacuum permittivity constant, n is the number of turns

The Attempt at a Solution

I already calculated force to be 2e-6.
There are 56.386 turns total because 23.3*2.42
so I got 2e-6/(4pi*10^-7*56.386)=0.02822
so 28.22 mA
I punched this in and it was wrong.
Did I do something weird?

 

[rude man]

Homework Statement

An electron circles at a speed of 8510 m/s in a
radius of 2.42 cm in a solenoid. The magnetic
field of the solenoid is perpendicular to the
plane of the electron’s path. Find the current in the solenoid if it has
23.3 turns/cm.
Answer in units of mA

Homework Equations

I think you can use B=uIN
I=B/(uN)
u is the universal vacuum permittivity constant, n is the number of turns

The Attempt at a Solution

I already calculated force to be 2e-6.
There are 56.386 turns total because 23.3*2.42
so I got 2e-6/(4pi*10^-7*56.386)=0.02822
so 28.22 mA
I punched this in and it was wrong.
Did I do something weird?

1. why calculate the force? your first task is to determine B. what relates B to q, m, v and R, all of which are given to you or known?

2. your calculation of no. of turns does not make sense to me. Your formula for B is correct if you replace N, the number of turns, by n, the no. of turns per unit length. n is also given to you.
Be careful to distinguish between N and n. When you have B you can calculate the current from that formula.

Watch your units!

 

[elitepro]

what relates B to q, m, v and R, all of which are given to you or known?

What equation relates these variables? I can't find one that does

 

[rude man]

How about centripetal force in circular motion = magnetic force?