Is a Velocity Dependent Force Always Non-conservative?

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A conservative force is defined by its independence from the path taken, which means it cannot depend on velocity since different velocities can result in different work done along the same path. The discussion highlights that while magnetic forces depend on velocity, they are considered conservative because they do no work on a charged particle moving perpendicular to the field. The key inquiry is how to mathematically demonstrate that a velocity-dependent force is non-conservative when it does perform non-zero work. The concept of curl is mentioned, but the focus is on establishing the conditions under which a force can be classified as conservative or non-conservative. Understanding these distinctions is crucial for analyzing forces in physics.
Gaudium
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Hi, I understand that a conservative force cannot depend on velocity, because by changing velocity we can do different work on the same path. But how can I show this mathematically, for a general force depending on velocity? Is the curl always zero for such a force?

Thank you?

Nese
 
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Are you sure about that? What about the force a magnetic field exerts on a moving charge?
 
Yeah, you are right. As far as I know some people see the magnetic force as a conservative force although it depends on velocity, because the work done by it on a particle is always zero. I do not know any other force with this property. Maybe I have to reformulate the question as how do we show that a velocity dependent force is not conservative, which has nonzer work on the particle?
 

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