How Do Magnetic Fields Affect Levitating Conductors and Current-Carrying Wires?

[Mspike6]

Hi..
I have 2 questions ( simple once i assure you :D) in Electromagntics.

1) ""A 0.120 m long copper wire has mass of 9.02 g and is carrying a current of 5.10 A perpendicular to a uniform magnetic field. This apparatus is placed in a strong magnetic field and the wire is found to levitate. Calculate the magnetic field Strength (B)"

Solution :

I actually solved this one right,
Fm=fg
I L B = Mg
B= mg/I L

What i don't understand is, why do we say that Fm=Fg if the wire Levitate ? i mean... if the why Levitate, it make sense that Fm is bigger (in magnitude) then Fg... why do we equalize them ??


My second questions


"Would two parallel wires carrying a current in opposite directions repel or attract one another?"


I think they would repel. but i don't know why :P




Thank, any help is really appreciated.

 

[MaxL]

As for why |magnetic force| = |gravitational force|-- Simple, if the magnetic force were bigger, the loop would accelerate upwards. Of course, if it did that, it would eventually leave the region of uniform magnetic field. (I think your issue may be with the word 'levitate.' I interpret that as 'hovering at a constant height.')

As for the two wires: If the current is going in opposite directions, the wires would repel. I figured that out by first drawing the wires, then doing the right hand rule to find the magnetic field at the second wire due to the first, then doing the right hand rule again to find the magnetic force on the second wire.

You can also think about it relativistically. An electon in one wire is moving in, say, the positive x direction. The other wire is lorenz contracted, but the electrons in that wire (moving in the negative x direction) are Lorenz contracted more than the stationary protons. The wire appears to have a negative net charge to the electrons in the first wire, and so they repel.

 

[Mspike6]

Thanks a lot Maxl..

and ya, i thought levitate means that it has a constant V > 0

Thanks

 

[MaxL]

Thank you for the great question. I love it when people finish their homework but still have questions!