MRI PHYSICS FOUNDATIONS · LESSON 03

Precession and the Larmor frequency.

Learn how fast hydrogen's net magnetization moves around B0 and why that speed matters.

About 7 minutesOne simple equation3 knowledge checks
B0M0
01EXPLAIN

MOVEMENT AROUND B0

Precession is a circular motion around the main field.

M0 does not simply point along B0. It can be modeled as moving around the B0 axis. This motion is called precession.

IN PLAIN LANGUAGEPrecession describes the way magnetization moves around B0, similar to the wobbling path of a spinning top.

The spinning top is a learning analogy for the collective magnetization. Individual proton spin is a quantum property and is not a tiny ball physically rotating.

02VISUALIZE

LEARN THE FREQUENCY WORDS

Frequency tells us how often a cycle repeats.

Hz

Hertz

One cycle per second.

MHz

Megahertz

One million cycles per second.

γ̄

Gyromagnetic ratio

A constant that is specific to the nucleus.

f0

Larmor frequency

The precession frequency at a given field strength.

03CONNECT

ONE RELATIONSHIP

A stronger field creates a higher frequency.

LARMOR RELATIONSHIPf0 = γ̄B0

For hydrogen, γ̄ is approximately 42.58 MHz/T.

0.55 T≈ 23.4 MHz

1.5 T≈ 63.9 MHz

3 T≈ 127.7 MHz

The relationship is direct. If B0 doubles from 1.5 T to 3 T, hydrogen's Larmor frequency also doubles.

WHY THIS MATTERS

The scanner must know hydrogen's frequency to deliver RF energy effectively. Gradients later create small, controlled frequency differences that help locate the signal.

04REMEMBER

THE SPEED LIMIT ANALOGY

B0 sets hydrogen's pace.

Think of field strength as setting the pace of precession. A higher B0 means a faster pace and therefore a higher Larmor frequency.

Remember: higher field, higher frequency.

05APPLY

CHECK YOUR UNDERSTANDING

Connect the motion to the equation.

What is precession?

It is the modeled motion of magnetization around the B0 axis.

What does the Larmor frequency describe?

It describes the precession frequency for a particular nucleus at a particular magnetic field strength.

If B0 doubles, what happens to hydrogen's Larmor frequency?

It doubles because Larmor frequency is directly proportional to B0.

LESSON 03 COMPLETE

You understand precession and the Larmor frequency.

Educational references

This lesson uses a simplified model to support learning and should be studied alongside formal MRI education.