Magnetic field and force and work

[miringains]

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Do both magnetic field, and magnetic force not do any work on charged particles, due to perpendicular movement?

 

[shaboobly]

It doesn't matter which instant you're choosing.

dW = (qv x B).v dt = 0

Regardless of the value of v or B at that point, the incremental value of work is zero.

ok im just gonna leave it at this because you still arent answering the question. the velocity in the force is different than the velocity in v dt. v dt represents the infinitesimal displacement caused by the force and the v that gives the value of the force is the original v, and isnt the same.

 

[deleted103644]

ok im just gonna leave it at this because you still arent answering the question. the velocity in the force is different than the velocity in v dt. v dt represents the infinitesimal displacement caused by the force and the v that gives the value of the force is the original v, and isnt the same.

NO IT ISN'T!!!

It's the same v.

 

[shaboobly]

NO IT ISN'T!!!

It's the same v.

why is it the same v? im just trying to understand this because newton's law, in my mind, says that the force -> acceleration -> different v in same direction of force and a, not the same as the original perpendicular v used to calculate the magnitude of the force.

i agree with everything else you say except for after this one specific instant, there is a force and displacement in the same direction and i dont see how there cant be because the particle is going to eventually create a circle, but at such a small part of the circle you can consider this displacement to be straight and in the same direction of the force...

 

[deleted103644]

You can rewrite the equation as this:

F = m*d^2s/dt^2 = q ds/dt x B.

You're trying to count instants - this stuff is happening at the same time and is constantly updating. That's the whole point of calculus - to be able to look at stuff like this. It's why Newton had to invent it to formulate his theories.

 

[V5RED]

yea i already said this is all true, but you didnt talk about the instant right after the first force is felt because like i already said and agree with you 100% the force will continue to change directions and induce circular motion and thus will have a type of centripetal acceleration which then implies there is no force in the direction of the displacement.

im talking about the very instant (i thought you would know because it seems you understand vectors and calculus pretty well) right after the first force is felt. it causes the particle to accelerate in the same direction because of newtons law, and once accelerated a velocity will be also in the same direction (like i said before and ill say again, there is another force that occurs once this velocity is initiated, which induces the circular motion aspect) and thus a small displacement will be made in the same direction also; this all implies non zero work at this instant.

here ill say it again: im not talking about the entire trajectory, just the instant after the original force is produced, not the second, not the third, not any other force, just the first force experienced at that very instant.

The magnetic force is the centripetal force. There is no separate force, it is all the same magnetic force the entire time. The only change is that as the particle changes direction, the force changes direction with it. Centripetal force is just a name for any force that induces uniform circular motion. The fancy centripetal force equation (Fc=mv^2/r) just tells you the magnitude of force needed to cause said motion.

Centripetal acceleration is different from regular acceleration like you would see in a falling ball or in an electron in an electrical field. Centripetal acceleration only affects the direction of a moving object, not its speed. Centripetal acceleration is perpendicular to the object's translational velocity. This perpendicular acceleration causes the circular motion. The object is never moving in the same direction as its centripetal acceleration.

In this example, there is no instant ever where magnetic force/acceleration or centripetal force/acceleration is in the same direction as velocity.

 

[shaboobly]

The magnetic force is the centripetal force. There is no separate force, it is all the same magnetic force the entire time. The only change is that as the particle changes direction, the force changes direction with it. Centripetal force is just a name for any force that induces uniform circular motion. The fancy centripetal force equation (Fc=mv^2/r) just tells you the magnitude of force needed to cause said motion.

Centripetal acceleration is different from regular acceleration like you would see in a falling ball or in an electron in an electrical field. Centripetal acceleration only affects the direction of a moving object, not its speed. Centripetal acceleration is perpendicular to the object's translational velocity. This perpendicular acceleration causes the circular motion. The object is never moving in the same direction as its centripetal acceleration.

In this example, there is no instant ever where magnetic force/acceleration or centripetal force/acceleration is in the same direction as velocity.

this answered my question exactly. i was treating the magnetic force as if it were tangential at that moment, but this cleared everything up. thanks.

 

[V5RED]

this answered my question exactly. i was treating the magnetic force as if it were tangential at that moment, but this cleared everything up. thanks.

Glad to have helped.

 

[Tatiana3325]

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[Tatiana3325]

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