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?

 

[HalfLostAndSearching]

Your attempt at a solution looks correct. However, it is always a good idea to double check your calculations and make sure that all units are converted correctly. In this case, the force you calculated should be in Newtons (N) and not in milliNewtons (mN). Also, make sure that the units for the magnetic field (B) are in Tesla (T) and not in milliTesla (mT). Once you have the correct units, your final answer should be in Amperes (A) instead of milliAmperes (mA).