Medical Device Simulators · Interactive Lab
Magnetic Resonance Imaging
Change the main magnetic field B₀ to observe the Larmor resonance frequency of hydrogen protons — the frequency an MRI scanner must transmit and receive at.
Parameters
Use the controls or enter precise values.
Why these controls?
Field strength is the main dial of MRI physics: the Larmor frequency f₀ = (γ/2π)·B₀ grows in direct proportion to B₀. Move it to see how 1.5 T and 3 T systems differ, and use the comparison field to put two field strengths side by side.
Calculated result
Larmor resonance frequency
Resonance frequency f₀
63.87
MHz
ω₀ = 2πf₀ = 4.0131e+8 rad/s
Field comparison
1.5 T
63.87 MHz
3.0 T
127.74 MHz
Frequency ratio: ×2.00 — equals the field ratio, because f₀ ∝ B₀.
- Frequency f₀
- 63.87 MHz
- Angular frequency ω₀
- 401.3 Mrad/s
f₀ is in megahertz (cycles per second); ω₀ is in radians per second. They differ by a factor of 2π — do not mix the two units.
Frequency vs. magnetic field
Linear through the origin — slope γ/2π ≈ 42.58 MHz/T
Formula
- f₀ = Larmor frequency in megahertz (MHz)
- B₀ = main magnetic field strength in tesla (T)
- γ/2π = gyromagnetic ratio of ¹H ≈ 42.58 MHz/T
- ω₀ = 2πf₀ = angular frequency in radians per second (rad/s)
Scope & assumptions
- This module shows only the resonance relationship f₀ = (γ/2π)B₀ for hydrogen protons — it does NOT produce an MRI image.
- The field is assumed perfectly uniform; real scanners have shim imperfections and gradient fields for spatial encoding.
- Chemical shift, relaxation (T1/T2), and RF pulse effects are not modelled.
- Other nuclei (¹³C, ³¹P, ²³Na) have different gyromagnetic ratios and resonate at different frequencies.