Why is the magnetic field perpendicular to the force?

[member 392791]

Hello, I was curious conceptually why the B field is perpendicular to the magnetic force. I know its a cross product, but is there some sort of conceptual argument that can convince me, other than shown by experiment.

Thanks

 

[mikeph]

The direction of the force also depends on the direction of the velocity of the electric charge. If you reverse the charge's velocity then the magnetic force points in the opposite way, for a given magnetic field. This can't be predicted if you define a magnetic field to be in the direction of the magnetic force.

 

[Philip Wood]

What an interesting question! Here are a few observations...

1. The original motivation for defining a magnetic field vector to have the direction it does, was no doubt so it matched the direction in which a compass needle (freely-pivoted magnet) pointed. Ampère showed that a plane current loop would orientate itself with its normal in the same direction as the compass needle pointed.

2. We can show that forces at right angles to the conductor forming the loop, all round the loop, give rise to a couple which will tend to orientate the loop just as stated in 1.

3. Special relativity gives a huge insight. I love the thought-experiment of two parallel wires (1 and 2) carrying currents in the same direction. In a frame of reference moving with the drift velocity, v, of the charge-carriers in 1, these charge carriers experience a purely E-field force from wire 2 (charge-carriers and fixed charges). Using simple relativistic ideas of time dilation and length contraction between frames, and not using the notion of B fields at all, we can show that (in the lab frame) wire 2 experiences a net force F proportional to v, attracting it to wire 1. And this force is equal to the magnetic force as conventionally calculated between parallel current-carrying wires!

Seen this way, the direction of the force on wire 1 is not in the least surprising.

[The thought experiment illustrates the key idea that an electromagnetic field has different electric field and magnetic field parts to it, depending on our reference frame.]

 

[vanhees71]

All this is very nicely described in "The Feynman Lectures" vol. 2.

 

[e.chaniotakis]

Hello,
Philip the nr.3 example is the BEST one could refer to in order to explain the magnetic force concept:)