How is Velocity Calculated in Lorentz Force Spectrometry?

[Big-Daddy]

If a particle of mass m and charge q (where q can be negative or positive, and the velocity should be positive if q is positive and negative if q is negative) is passed through an electric field of potential V_d, what is the velocity v of the particle?

Or possibly this should be a vector problem? Maybe I need to specify some angles? If you'd take me through what's going on here I'd be grateful, and if there are some angles of incidence I should have given but didn't then please give them algebraic letters anyway and proceed.

 

[berkeman]

If a particle of mass m and charge q (where q can be negative or positive, and the velocity should be positive if q is positive and negative if q is negative) is passed through an electric field of potential V_d, what is the velocity v of the particle?

Or possibly this should be a vector problem? Maybe I need to specify some angles? If you'd take me through what's going on here I'd be grateful, and if there are some angles of incidence I should have given but didn't then please give them algebraic letters anyway and proceed.

What is the context of your question? Is this for schoolwork? What references are you using so far to understand the Lorentz force?

 

[Big-Daddy]

No I'm asking this question for my own understanding. The topic is mass spectrometry and my reference so far is this document:

http://www.whoi.edu/cms/files/Lecture6_2011_96624.pdf

Everything makes sense except for the velocity as a function of mass, V and charge expression. And in general, the problem I see with the whole thing is that it would appear to treat negatively charged particles the same way as positively charged particles (either that, or say that they have the same velocity).

 

[Big-Daddy]

My final goal is to figure out how, in a mass spectrometer, we can transform the time taken for each ion to reach the detector, into the mass/charge value for that ion.

 

[sardar]

Lorentz force spectrometry is a technique used to analyze the properties of charged particles, such as their mass and charge, by measuring the forces acting on them in an electric and magnetic field. In this scenario, a particle with mass m and charge q is passing through an electric field of potential Vd.

To determine the velocity v of the particle, we can use the Lorentz force equation, which states that the force (F) acting on a charged particle in an electric and magnetic field is equal to the product of its charge (q) and the electric field (E) plus the cross product of its charge and velocity (v) with the magnetic field (B).

Mathematically, this can be written as F = q(E + v x B). Since we are only considering an electric field in this scenario, the equation simplifies to F = qE. The force acting on the particle will cause it to accelerate, and the velocity of the particle can be calculated using the equation F = ma, where m is the mass of the particle and a is its acceleration.

Therefore, the velocity v of the particle can be calculated as v = (qE)/m. The direction of the velocity will depend on the direction of the electric field and the charge of the particle. If q is positive, the velocity will be in the same direction as the electric field, and if q is negative, the velocity will be in the opposite direction.

In order to fully understand the motion of the particle, it is important to also consider the magnetic field and the angle of incidence. The angle of incidence, denoted by theta (θ), is the angle between the velocity vector and the electric field vector. This angle will affect the magnitude and direction of the force acting on the particle.

In conclusion, the velocity v of a charged particle passing through an electric field of potential Vd can be calculated using the Lorentz force equation, taking into consideration the particle's mass, charge, and the direction of the electric field. The angle of incidence can also play a role in determining the particle's velocity.