Magnetic radiation reaction force

Key takeaways

Magnetic radiation reaction force belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Magnetic radiation reaction force to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Magnetic radiation reaction force from memory before moving on to harder problems.

Reference excerpt

The magnetic radiation reaction force is a force on an electromagnet when its magnetic moment changes. One can derive an electric radiation reaction force for an accelerating charged particle caused by the particle emitting electromagnetic radiation. Likewise, a magnetic radiation reaction force can be derived for an accelerating magnetic moment emitting electromagnetic radiation. Similar to the electric radiation reaction force, three conditions must be met in order to derive the following formula for the magnetic radiation reaction force. First, the motion of the magnetic moment must be periodic, an assumption used to derive the force. Second, the magnetic moment is traveling at non-relativistic velocities (that is, much slower than the speed of light). Finally, this only applies this force is proportional to the fifth derivative of the position as a function of time ("crackle"). Unlike the Abraham–Lorentz force, the force points in the direction opposite of the crackle.

Definition and description Mathematically, the magnetic radiation reaction force is given by, in SI units:

F r a d = − μ 0 q 2 R 24 π c 3 d 3 a → d t 3 {\displaystyle \mathbf {F} _{\mathrm {rad} }=-{\frac {\mu _{0}q^{2}R}{24\pi c^{3}}}{\frac {\mathrm {d} ^{3}{\vec {a}}}{\mathrm {d} t^{3}}}}

where:

F is the force,

d 3 a → d t 3 {\displaystyle {\frac {\mathrm {d} ^{3}{\vec {a}}}{\mathrm {d} t^{3}}}} is the crackle (the third derivative of acceleration, or the fifth derivative of displacement), μ0 is the permeability of free space, c is the speed of light in free space q is the electric charge of the particle. R is the radius of the magnetic moment Note that this formula applies only for non-relativistic velocities. Physically, a time changing magnetic moment emits radiation similar to the Larmor formula of an accelerating charge. Since momentum is conserved, the magnetic moment is pushed in the direction opposite the direction of the emitted radiation. In fact the formula above for radiation force can be derived from the magnetic version of the Larmor formula, as shown below.

Background In classical electrodynamics, problems are typically divided into two classes:

Problems in which the charge and current sources of fields are specified and the fields are calculated, and The reverse situation, problems in which the fields are specified and the motion of particles are calculated. In some fields of physics, such as plasma physics and the calculation of transport coefficients (conductivity, diffusivity, etc.), the fields generated by the sources and the motion of the sources are solved self-consistently. In such cases, however, the motion of a selected source is calculated in response to fields generated by all other sources. Rarely is the motion of a particle (source) due to the fields generated by that same particle calculated. The reason for this is twofold:

Neglect of the "self-fields" usually leads to answers that are accurate enough for many applications, and Inclusion of self-fields leads to problems in physics such as renormalization, some of which still unsolved, that relate to the very nature of matter and energy. This conceptual problems created by self-fields are highlighted in a standard graduate text. [Jackson]

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Worked examples

Example 1 — a first encounter with Magnetic radiation reaction force

Start with the simplest possible case. Write down what Magnetic radiation reaction force claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Magnetic radiation reaction force before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Magnetic radiation reaction force ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Magnetic radiation reaction force

In research: Magnetic radiation reaction force appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Magnetic radiation reaction force in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Magnetic radiation reaction force is common in secondary-school and first-year university syllabi. It links to neighbouring topics Electrodynamics, Electromagnetic radiation, so understanding it makes those chapters shorter.
In everyday life: Look for Magnetic radiation reaction force outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Magnetic radiation reaction force in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Magnetic radiation reaction force means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Magnetic radiation reaction force out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Magnetic radiation reaction force in simple terms?

The magnetic radiation reaction force is a force on an electromagnet when its magnetic moment changes. One can derive an electric radiation reaction force for an accelerating charged particle caused by the particle emitting electromagnetic radiation.

Why does Magnetic radiation reaction force matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Magnetic radiation reaction force?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Magnetic radiation reaction force.