MadSci Network: Physics
Query:

Re: Lorentz force on a Helmholtz coil exerted from a conductor

Date: Sat Dec 3 14:11:40 2005
Posted By: Prater Brian D., Staff, Magnetics, Cavetronics R&D labs
Area of science: Physics
ID: 1131533745.Ph
Message:

B = žo (4/5)3/2 N I /A 

žo is the permeability of free space

N is the number of turns in the Helmholtz coil

I is the coil current

A is the radius of the coil

Theory 
A charged particle (qo) moving with velocity v in a magnetic field B feels 
the force (Called the Lorentz Force): F = qov x B. 
Since v and B are perpendicular, and since the charged particle in an 
electron, replacing qo with e => FB = evB. 
The B field is uniform therefore the electron moves in a circular 
trajectory. 
Also, since the electron moves in a circle with constant v , it undergoes 
Uniform Circular Motion => a centripetal force (Fc = m v2 / R) . 

Setting Fc = FB => m v2 / R = evB => m v = e B R 5.1), where R is the 
radius of the electronís circular trajectory. 



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