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Dash-IQ
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When a wire has current I in a magnetic field B, there is the Lorentz force is it considered a conservative force or not? Please do explain as to why it is.
UltrafastPED said:The force on the wire is given here: http://en.wikipedia.org/wiki/Lorentz_force#Force_on_a_current-carrying_wire
If the electric field is static then it's curl is zero - and the electric field is conservative.
But when we consider the magnetic field Maxwell's equations tell us that it's divergence is always zero -so if it's curl were also zero we would have B=0. Thus the magnetic field is not conservative, and the exact situation shouldn't matter.
Dash-IQ said:When a wire has current I in a magnetic field B, there is the Lorentz force is it considered a conservative force or not? Please do explain as to why it is.
Robert_G said:now for the Lorentz force, this force actually has something to do with the velocity of the charged particles. Different velocity means Different force, that plane will never be introduced. So it's not conservative.
DrStupid said:Lorentz force is conservative because the work done between two points is independent from the path.
Dash-IQ said:Hm, what about the statements of the rest?
UltrafastPED said:Read #2 again. What is your conclusion?
DrStupid said:I conclude that we need to distinguish between Lorentz force and magnetic field. As Lorentz force has no force field the corresponding formalisms does not apply. Thus there is only one condition left: conservative forces conserve mechanical energy.
BruceW said:But what happens when we integrate this force, over the path of the particle? What happens to the term due to the magnetic field?
BruceW said:But what happens when we integrate this force, over the path of the particle? What happens to the term due to the magnetic field?
That is wrong.Robert_G said:If the force is only depends on the position, or in other words.
[itex]\mathbf{F}=\mathbf{f(\mathbf{r})}[/itex],
then, is conservative. because, only if the force only depends on [itex]\mathbf{r}[/itex], A plane with the equal potential energy can be introduced.
The Coulomb force has zero divergence and curl.UltrafastPED said:The force on the wire is given here: http://en.wikipedia.org/wiki/Lorentz_force#Force_on_a_current-carrying_wire
If the electric field is static then it's curl is zero - and the electric field is conservative.
But when we consider the magnetic field Maxwell's equations tell us that it's divergence is always zero -so if it's curl were also zero we would have B=0. Thus the magnetic field is not conservative, and the exact situation shouldn't matter.
why is that wrong? It is a different definition of conservative force. But I've seen more than one definition used. For example, on the wikipedia page, they seem to use at least two different definitions.Meir Achuz said:That is wrong.
BruceW said:why is that wrong?
It is the two onlys that make that statement wrong. The equation given is for a conservative force, but there are many other examples of conservative forces. One example, among many, is the force in my previous post.Robert_G said:No, It's not, there is an easy way to see if a force is conservative, or not. If the force is only depends on the position, or in other word.
[itex]\mathbf{F}=\mathbf{f(\mathbf{r})}[/itex],
then, is conservative. because, only if the force only depends on [itex]\mathbf{r}[/itex], A plane with the equal potential energy can be introduced.
now for the Lorentz force, this force actually has something to do with the velocity of the charged particles. Different velocity means Different force, that plane will never be introduced. So it's not conservative.
Dissipative forces like [itex]{\bf F}=-k({\bf v\cdot r)r}[/itex] are not conservative.Khashishi said:All fundamental forces are conservative. The Lorentz force is just the electromagnetic force, which is conservative.
ah right. The force field would also need to have zero curl, to be able to write it as a gradient of a potential energy.DrStupid said:Counterexample: F = [x-z,y,0]
The Lorentz force is the force experienced by a charged particle in the presence of an electric and magnetic field. It is given by the equation F = q(E + v x B), where q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field.
No, the Lorentz force is not conservative. This means that the work done by the force on a particle depends on the path taken by the particle, not just its initial and final positions. In other words, the work done by the Lorentz force is not independent of the path taken by the particle.
We can prove that the Lorentz force is not conservative by calculating the line integral of the force along a closed path. If the line integral is not equal to zero, then the force is not conservative. In the case of the Lorentz force, the line integral is equal to the change in kinetic energy of the particle, which is not zero.
The fact that the Lorentz force is not conservative has important implications in electromagnetism. It means that the work done by the force cannot be expressed as the difference in a potential function. This also means that the concept of potential energy cannot be applied to charged particles in electric and magnetic fields.
Since the Lorentz force is not conservative, the work done on a charged particle is dependent on the path taken by the particle. This can result in complex and unpredictable motion of charged particles in electric and magnetic fields. It also means that the energy of the particle is not conserved, as work is done on the particle by the non-conservative force.