Angular momentum in ElectroMagnetic fields(Feynman's Disk Paradox)

In summary, in Griffiths' "Introduction to Electrodynamics" book, example 8.4 discusses the angular momentum density calculation for a version of Feynman disk paradox. The resulting angular momentum points in the z direction, but if we assume that the r vector has components in both the s and z directions, the angular momentum density will have both a z component and an s component. This s component is not constant, but the total angular momentum must have only a z component in order for the cylinders not to tip over. It appears that there is no error in your reasoning, and that Griffths may have neglected the \hat{s} component. Additionally, the total angular momentum of the EM field does not have an xy component
  • #1
Henriamaa
14
1
In Griffiths book, "Introduction to Electrodynamics" example 8.4 he calculates the angular momentum density for a set up that is a version of Feynman disk paradox. His answer for the angular momentum points in the z direction. But if we you assume that the r vector has component in the s direction and z direction(I am almost sure this is correct) [itex]\vec{r}[/itex] = s[itex]\hat{s}[/itex]+ z[itex]\hat{z}[/itex], then the angular momentum density has both a z component and s component. The s component is not constant. The total angular moment on the other hand has to end up with only z component or the cylinders would tip over. Where is the error in my reasoning?
 
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  • #2
It seems to me you've made no error. The angular momentum density should in fact have an [itex]\hat{s}[/itex] component for [itex]z \neq 0[/itex]. It seems Griffths neglected this. However, there is no xy component of the total angular momentum of EM field; it cancels out in via integration.
 
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Related to Angular momentum in ElectroMagnetic fields(Feynman's Disk Paradox)

1. What is the Feynman's Disk Paradox?

The Feynman's Disk Paradox is a thought experiment proposed by physicist Richard Feynman to illustrate the concept of angular momentum in electromagnetic fields. It involves a spinning disk with a conducting rim placed in a uniform magnetic field, causing the disk to spin faster and faster without an apparent source of energy.

2. How does the Feynman's Disk Paradox relate to angular momentum?

The Feynman's Disk Paradox demonstrates the conservation of angular momentum in electromagnetic fields. According to this principle, the total angular momentum of a system remains constant unless an external torque is applied. In this experiment, the spinning disk experiences a torque due to the interaction between the magnetic field and the current induced in the disk's conducting rim, resulting in an increase in its angular momentum.

3. What is the explanation for the increase in the disk's angular momentum?

The increase in the disk's angular momentum can be explained by the Lenz's law, which states that the direction of an induced current is such that it opposes the change that caused it. In this case, the induced current in the disk's conducting rim creates a magnetic field that opposes the external magnetic field, causing a torque that accelerates the disk's rotation.

4. Is the increase in the disk's angular momentum perpetual?

No, the increase in the disk's angular momentum is not perpetual. Eventually, the disk will reach a maximum angular velocity and will stop accelerating. This is because as the disk spins faster, the induced current in the conducting rim produces a stronger magnetic field that counteracts the external magnetic field, resulting in a decrease in the torque and ultimately causing the disk to reach a steady-state rotation.

5. How does the Feynman's Disk Paradox relate to real-world applications?

The Feynman's Disk Paradox has real-world applications in various fields, including electrical engineering and electromechanics. It is used in devices such as electric motors, generators, and gyroscopes, which rely on the principles of electromagnetic induction and angular momentum to function. Understanding this paradox is crucial in designing and optimizing these technologies.

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