Mass Spectrometry Explained: How F=qVXB Works

By Pankaj Kumar|Last Updated: July 12, 2026|

Key Takeaways

Mass spectrometry measures the mass-to-charge ratio of ions analytically.
The magnetic force equation F=qVXB governs how ions bend in the spectrometer.
Ions are generated by bombarding a sample with fast-moving electrons.
Heavier ions bend less, producing a larger radius in the magnetic field.
A mass spectrum plots intensity against the mass-to-charge ratio.

This article will see how mass spectrometry works and how the force equation F=qVXB can answer the question. Students working through electromagnetism topics may also find it useful to connect with a Java tutor for related computational coursework.

What is Mass Spectrometry?

Mass Spectrometry Definition

It is a technique used to measure the mass-to-charge m/q or q/m ratio of ions analytically. We present the result as a mass spectrum — a plot of intensity vs the q/m ratio.

Schematic diagram of a mass spectrometer showing key components

Image courtesy: BronkHorst

Introduction to Mass Spectroscopy and the Use of F=qVXB

The force (magnetic) on a charged particle is F=qVBsin(θ) in scalar notation, and in vector notation, it is F=qVXB where X is the cross product and F, V, B are vector quantities. The symbols have their usual meanings.

F = magnetic force

V = Velocity

B = External magnetic field

q = charge

θ = angle that velocity vector makes with the external magnetic field B.

Identifying the Charge q That Is Moving

We bombard the sample with fast-moving electrons and generate charge q. The moving electrons hit the sample atoms and knock out electrons from their outer shells, making the sample atoms charged. This charge is necessary because we cannot impart high speed using the high potential difference unless the atoms are charged.

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Identifying the Velocity That Describes the Motion of the Charge

We apply a very strong EMF to the sample, converting it to ions. It imparts a force on the ions given by F=qE, where E is the electric field associated with the applied potential.

Let it move by a distance d in this electric field E, so work done is qEd. This work must equal the change in kinetic energy as energy is not lost anywhere. So 1/2mV^2 = qEd, which gives us V = (2qEd/m)^0.5. It is how the velocity comes into the picture.

Identifying the Magnetic Field B That the Charge Feels

We apply an external magnetic field to the setup via high-power electromagnets. This B is normal to the motion of the charges (θ = 90 degrees, so sin(θ) = 1).

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Calculation of Net Force

We saw that F = qVXB. The variables are defined as follows:

q = charge on the ion

V = (2qEd/m)^0.5 as calculated earlier.

B = External magnetic field, which acts at θ = 90 degrees (normal) to the velocity vector.

Using the vector cross product rule, F magnetic is F = qVBsin90 = qVB. The direction is normal to the plane containing both V and B vectors and is determined by the right-hand rule.

F = qB(2qEd/m)^0.5

Explanation of This Force F in Context of the Problem

Force F is equal to m*V^2/r where r = radius of the circle in which the ions bend when they pass through the external magnetic field. So:

qBV = m*V^2/r

Using this, we can get r = mv/qB where V = (2qEd/m)^0.5.

We can see clearly that except for mass “m,” all the things are the same for each ion. The ion with more mass will have a larger radius “r” and will bend lesser. Using this, we can determine the kind of mass distribution the sample has. We see the density on the detector to make out the fraction of ions which bent more or less.

A typical mass spectrometry spectra is shown below for reference.

mass spectrometry spectra showing intensity vs mass-to-charge ratio

So this was the theory behind mass spectrometry. If something is not clear, feel free to comment in the comment section below. We will be happy to answer all your questions.

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