# How does magnet follow both law at same time newton 3rd law but also magnetic field?

have been wondering a question that:-

It is said that " magnet(say,Magnet no.1) has a magnetic field that informs in which direction the north pole (of other magnet or compass say , magnet no.2) will point"

But doesn't that magnet no. 2 which is placed in magnetic field of magnet no.1, also have its own magnetic field which can deflect magnet no. 1 too!

Than , we also know about newton's 3rd law "every action has an equal and opposite reaction"

So according to this , magnet 1 and magnet 2 will be feeling same force but in opposite direction. Than their respective north poles should be facing in opposite direction.

But according to diagram I draw it is not following my assumption:-

enter image description here

Here,

Lighter dotted line is magnetic field of magnet no.1

Darker dotted line is magnetic field of magnet no.2

Arrow depicting the calculated direction of their north pole due to magnetic field

(Negleting the drawing mistake that I intersect field lines , I am just talking about the direction of north pole 'should' be according magnetic field )

But look! Direction of arrow are not in opposite direction as according to newton's 3rd law. Do magnet obey law? Along with obeying the the direction according to magnetic field?

So question is:-

when two magnets are kept in close to each other How do they will follow both laws I.e deflecting north pole according to magnetic field also newton's 3rd law? If possible support with a rough diagram

• Newtons third law isn't actually correct. Electrodynamics completely disproves newtons third law. Jan 1, 2022 at 16:37
• @jensenpaull I couldn't disagree more. Jan 4, 2022 at 19:12
• In general, magnetic forces do not obey Newton's Third Law. Indeed, they cannot, since Newton's Third Law is incompatible with special relativity, because it talks about the forces on two separated bodies at the same instant. But you can't pin down what it means to be at the same time for two different bodies; that's the relativity of simultaneity. What does generalize to relativity is momentum conservation (which is a consequence of Newton's Third Law in classical mechanics); however, even there, things can be tricky, since the momentum of the electromagnetic field must be included.
– Buzz
Jan 5, 2022 at 0:20

## 2 Answers

The atomic dipoles in a ferromagnetic material are subject to a torque which tends to align them with the resultant magnetic field in their region, and a net force which is proportional to the gradient of the field. As a result, the North (seeking) poles of two magnets tend to repel each other (as do the South poles) and a north and South pole attract each other. The forces do form equal and opposite pairs. If the magnets in your sketch are free to move, both will rotate and translate, bringing the South pole of the upper magnet and the North pole of the other toward each other.

The force that was drawn on the horizontal is acting on the "south" end of the magnet. This force should be in the opposite direction since the force that you are trying to represent is coming from the "north" of the vertical magnet. If this method of drawing the force tangent to the field lines is used on the "north" end of the horizontal magnet then this method would work. This the diagram that was provided had the force on both the "north" and "south" pole of the horizontal magnet it would appear that the vertical magnetic field from the vertical magnet is trying to rip the horizontal magnet in half. If this was set up in a way that the vertical magnet was fixed and the horizontal magnet was free to rotate it would rotate to align with the vertical magnet. So that the "south" pole is closest to the "north" of the vertical magnet.