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maeila
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Why is angular momentum conserved for a charge in an electric field?
maeila said:Is the velocity of a charge q moving in an electric field generated by Q inversely proportional to the distance r from q to Q? And if so, why?
maeila said:Why is angular momentum conserved for a charge in an electric field?
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Angular momentum (rarely, moment of momentum or rotational) is the rotational equivalent of linear momentum. It is an important quantity in physics because it is intrinsically conserving quantity --the total angular momentum of a system remains constant unless acted on by an external force torque.
https://en.m.wikipedia.org/wiki/Angular_momentumIf You haven't read this article, you could read the pertinent areas of this Wiki Art angular "Conservation of Angular momentum" - - "angular momentum in Orbital mechanics" and '--- "The Law of Areas"maeila said:I don't know, I just can't see how the relation between distance and velocity could justify that.
It made sense in the gravitational field, since when a satellite gets closer it also gets faster. Now, if I have a stationary positive charge and a smaller positive charge in its field, the first charge will accelerate the other to repel it, so with the increasing distance of the second charge there's also an increase in velocity.
Well, if the small charge has no initial velocity it will move along a radial direction and the angular momentum will be zero in any position. The angle alpha in your formula is zero. If it has some non-radial component it will have some angular momentum (in respect to the fixed charge). But the electrostatic force is always radial so there will be no torque applied (again, relative to the origin attached to the fixed charge) and no change in the angular momentum.maeila said:I don't know, I just can't see how the relation between distance and velocity could justify that.
It made sense in the gravitational field, since when a satellite gets closer it also gets faster. Now, if I have a stationary positive charge and a smaller positive charge in its field, the first charge will accelerate the other to repel it, so with the increasing distance of the second charge there's also an increase in velocity.
Conservation of angular momentum for charges is a fundamental principle in physics that states that the total angular momentum of a system of charges remains constant in the absence of external torques.
Angular momentum for charges is defined as the product of the charge's linear momentum and its distance from a chosen axis of rotation.
Conservation of angular momentum is important because it is a fundamental law of nature that governs the behavior of charged particles in motion. It helps us understand and predict the behavior of objects in rotational motion.
One example is the behavior of a spinning top. As long as there are no external torques acting on the top, its angular momentum will remain constant. Another example is the orbit of an electron around the nucleus of an atom, which also follows the principle of conservation of angular momentum.
No, conservation of angular momentum for charges is a fundamental law of physics and has been observed to hold true in all known cases. Violations of this principle would require a violation of the laws of physics themselves.