# Question about conservation of angular momentum for charges

maeila
Why is angular momentum conserved for a charge in an electric field?

Staff Emeritus
Why wouldn't it be?

maeila
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?

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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?

No. Force and hence acceleration are governed by the inverse square law. Not velocity.

maeila
Then how is the quantity L=qvr sin(a) conserved?

Homework Helper
What is the trajectory of you particle?

Gregory Alan
Why is angular momentum conserved for a charge in an electric field?
[/QUO
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.

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maeila
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.

Gregory Alan
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.
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"

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Homework Helper
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.