# The work of magnetic force on the wire

hokhani
When the two current carrying wires (with identical current directions) attract each other, it seems that the magnetic field of wires do work while we know that magnetic force is perpendicular to the velocity of charge. I would like to know whether the the two wires get closer or not? What about the neutralizing force of transverse electric field of accumulated charge across the wire (as occurs in Hall effect)?

Gold Member
When the two current carrying wires (with identical current directions) attract each other, it seems that the magnetic field of wires do work while we know that magnetic force is perpendicular to the velocity of charge. I would like to know whether the the two wires get closer or not? What about the neutralizing force of transverse electric field of accumulated charge across the wire (as occurs in Hall effect)?
It is interesting that the two forces oppose each other but do not usually balance.
In the old cgs system of units, the forces were used to define the units of electric and magnetic field strength. Maxwell noticed that their ratio was equal to the speed of light, and this led him to suppose that light was electromagnetic.

hokhani
It is interesting that the two forces oppose each other but do not usually balance.
Could you please tell which two forces; The forces between the two wires (action and counteraction) or the transverse electric force and magnetic force on the moving charges?

Gold Member
Could you please tell which two forces; The forces between the two wires (action and counteraction) or the transverse electric force and magnetic force on the moving charges?
Sorry I misunderstood your original question. The Hall effect is surely very small - we know from observation that wires attract.

Homework Helper
Gold Member
It appears as the magnetic field does work here but this is NOT true. A more careful examination of the hall effects involved, reveals that the work is done by the electric field (electrostatic forces between the stream of electrons and the surface charge build up of hall effect). I had made a threat where I explain this in detail. Give me a sec to locate it

hokhani and vanhees71
sweet springs
Two wire are coming closer with increasing kinetic energy that is supplied with battery, not from magnetic field generated by the current, I think.Battery works. Magneric field does not work.
Direction of current electrons is curved and deviated by magnetic field. Electrons are constrained within wire. As a simple model electrons collide with wire surface boundary and transmit momentum and energy to wire body. Battery provide energy to help electrons have their original speed relative to wire body. This is interpreted as increase of resistance of wire.
So we may say batteriy lasts longer when wire is alone than there is another current wire nearby.

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Delta2
Homework Helper
Gold Member
Two wire are coming closer with increasing kinetic energy that is supplied with battery, not from magnetic field generated by the current, I think.Battery works. Magneric field does not work.
Direction of current electrons is curved and deviated by magnetic field. Electrons are constrained within wire. As a simple model electrons collide with wire surface boundary and transmit momentum and energy to wire body. Battery provide energy to help electrons have their original speed relative to wire body. This is interpreted as increase of resistance of wire.
So we may say batteriy lasts longer when wire is alone than there is another current wire nearby.

I have my doubts about momentum because internal forces cannot change the overall momentum of a system ( the wire is a system of electrons+positive ions) but yes I believe the force between the electrons and the surface charges at the boundary of wire is what does the work, as internal forces can do work.
I believe the magnetic field force is responsible for the change in momentum of the wire, but internal forces between electrons and ions are responsible for the change in kinetic energy of the wire.

hokhani
I think the electrons immediately become gathered by magnetic force on one side of the wire and the electric force of them on the moving electrons cancels the magnetic force and so the moving electrons can go in a straight line without deviation. However, the reaction electric force of these non-deviated electrons, on the electrons gathered on the side of the wire, causes motion of the wire. Therefore, it is the electric field that does work.
On the other hand, we expect the gathered electrons on the sides of the two wires repel each others (suppose the same direction of currents for the two wires) and so a repulsion force between the two wires. It seems a discrepancy here, because on one hand, we expect the two wires become closer but on the other hand they repel each other. The third possibility is that these two forces cancel each other and the wires remain fixed without moving.

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Delta2
Homework Helper
Gold Member
I think the electrons immediately become gathered by magnetic force on one side of the wire and the electric force of them on the moving electrons cancels the magnetic force and so the moving electrons can go in a straight line without deviation. However, the reaction electric force of these non-deviated electrons, on the electrons gathered on the side of the wire, causes motion of the wire. Therefore, it is the electric field that does work.
I agree completely with the above
On the other hand, we expect the gathered electrons on the sides of the two wires repel each others (suppose the same direction of currents for the two wires) and so a repulsion force between the two wires. It seems a discrepancy here, because on one hand, we expect the two wires become closer but on the other hand they repel each other. The third possibility is that these two forces cancel each other and the wires remain fixed without moving.
That repulsion force (assuming same direction of current for the two wires) is small compared to the Laplace force. However if the wires are placed very close then this repulsion force might not be negligible. But when the wires are placed too close, the Laplace force becomes bigger as well. Maybe it is safe to say that the repulsion force is negligible in comparison to the Laplace Force.

hokhani
I agree completely with the above

That repulsion force (assuming same direction of current for the two wires) is small compared to the Laplace force.
Both Laplace and repulsion forces become stronger as the wires get closer. It seems that these two forces cancel each other. We should see, by experiment, what really happens when the two current-carrying wires are placed close together. I haven't tried this experiment, so far.

sweet springs
I have my doubts about momentum because internal forces cannot change the overall momentum of a system ( the wire is a system of electrons+positive ions)

Yea I feel uneasiness about Newton's third law concerning Lorentz force. Say Lorentz force push electron as action, as reaction electron push what ? EM field must be the answer but how it actually is?

$$\frac{d}{dt}[\ p^\alpha+\frac{1}{c^2}\int N^\alpha dv\ ]=\int T^{\alpha\beta}dS_\beta$$