Lorentz Force
Claimed by Firas Sheikh--Fsheikh6 (talk) 21:09, 1 November 2015 (EST)
The Main Idea
The Lorentz Force is the combination of the Electric and Magnetic Forces. Basically the Lorentz Force is applied as a net force on a particle or number of particles when both electric and magnetic fields are present.
A Mathematical Model
[math]\displaystyle{ \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B} }[/math] where qE is the electric force and qv x B is the magnetic force.
A Computational Model
Examples
Be sure to show all steps in your solution and include diagrams whenever possible
Simple
The magnitude of the Electric Force at a certain point in space is 3e-9 and the magnitude of the Magnetic Force at that same point is -7e-9. What is the Lorentz Force at this point in space?
Force Lorenz = 3e-9 - 7e-9 = -4e-9 Newtons.
Middling
Find the Lorentz Force on an electron given that the magnitude of the Electric Field at a point in space is 4e-6 N/C and the magnitude of the magnetic field at that same point is 8e-7 T and the speed of the electron is 6000 m/s.
Force Electric = qE =(-1.6e-19)*(4e-6) = -6.4e-25 N Force Magnetic = q*B*v =(-1.6e-19)*(8e-7)(6000) = -7.68e-22 N Force Lorentz = Force Electric + Force Magnetic = -7.69 e-22 N
Difficult
An electron is 4e-9 m away from another electron. The magnetic field in the region is 4e3 T and the velocity of the electron is 40000 m/s. What is the Lorentz force on the electron.
Electric Force = (9e9)((1.6e-19*1.6e-19)/((4e-9)^2)) = 1.44e-11 N
Magnetic Force = (1.6e-19)*(4e3*40000) = 2.56 e-11 N
Lorentz Force = 2.56e-11 +1.44e-11 = 4e-11 N
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