What Are the Correct Units for the Larmor Formula?

In summary, the Larmor formula calculates the amount of power emitted by an accelerated charge. When checking the units, it was found to be in [kg m^2 s^-1], but it should actually be in [kg m^2 s^-3] if it is measured in watts. The error was due to the unit of acceleration being mistakenly written as m/s instead of m/s^2.
  • #1
bdforbes
152
0
The Larmor formula is:

[tex]P=\frac{\mu_0 q^2 a^2}{6\pi c}[/tex]

When I checked the units of this, I got [kg m^2 s^-1]. If it is in watts, shouldn't it be [kg m^2 s^-3]? I was pretty thorough in putting everything in SI units.

[tex]\mu_0[/tex] is N/A^2 or kg m s^-2 A^-2.
[tex]q^2[/tex] is C^2 or A^2 s^2
[tex]a^2[/tex] is m^2 s^-2
c is m s^-1

Have I made a stupid error, or is this just the wrong way of doing the dimensional analysis?

This is not homework.
 
Physics news on Phys.org
  • #2
I don't think the formula is right.

edit: Never mind. :P
 
Last edited:
  • #3
The units of acceleration are [itex]m/s^2[/itex] not [itex]m/s[/itex], so the units of [itex]a^2[/itex] are [/itex]m^2/s^4[/itex] not [/itex]m^2/s^2[/itex].
 
  • #4
Stupid error it is then, thanks :P. You'd think after 4 years of uni I might be able to get that one right...
 

1. What is the Larmor formula?

The Larmor formula, also known as the Larmor frequency or Larmor precession, is a fundamental equation in electromagnetism that describes the precessional motion of a charged particle in a magnetic field.

2. What are the dimensions of the Larmor formula?

The dimensions of the Larmor formula can be derived from its equation, which is given by ω = qB/m, where ω represents the Larmor frequency, q is the charge of the particle, B is the magnetic field strength, and m is the mass of the particle. Therefore, the dimensions of the Larmor formula are [T^-1], or inverse seconds.

3. How is the Larmor formula used in scientific research?

The Larmor formula is used in a variety of scientific research fields, including nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), and particle accelerators. It is also used to calculate the frequency of electromagnetic radiation emitted by charged particles in a magnetic field.

4. What is the relationship between the Larmor frequency and the gyromagnetic ratio?

The Larmor frequency is directly proportional to the gyromagnetic ratio, which is a fundamental property of a particle that determines its behavior in a magnetic field. The gyromagnetic ratio is given by γ = q/m, where q is the particle's charge and m is its mass. Therefore, the higher the gyromagnetic ratio, the higher the Larmor frequency.

5. What are some real-world applications of the Larmor formula?

The Larmor formula has many practical applications, such as in MRI machines used in medical imaging, nuclear reactors, and particle accelerators. It is also used in the study of the Earth's magnetic field and in determining the properties of materials in solid-state physics.

Similar threads

  • Classical Physics
Replies
7
Views
745
  • Classical Physics
Replies
1
Views
832
Replies
2
Views
1K
  • Classical Physics
Replies
1
Views
824
  • Classical Physics
Replies
3
Views
1K
Replies
68
Views
3K
  • Introductory Physics Homework Help
Replies
7
Views
143
  • Classical Physics
Replies
21
Views
1K
  • Introductory Physics Homework Help
Replies
16
Views
917
Replies
21
Views
1K
Back
Top