Why is the magnetic field perpendicular to the force?

In summary, the direction of the magnetic force is perpendicular to the B field due to its relationship with the velocity of the electric charge. This was originally observed through the direction of a compass needle and further explained through Ampère's experiments. Additionally, the concept can be understood through special relativity and the thought experiment of two parallel wires. All of this is explained in "The Feynman Lectures" vol. 2.
  • #1
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
 
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  • #2
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.
 
  • #3
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.]
 
  • #4
All this is very nicely described in "The Feynman Lectures" vol. 2.
 
  • #5
Hello,
Philip the nr.3 example is the BEST one could refer to in order to explain the magnetic force concept:)
 

What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges or by the intrinsic magnetic moments of elementary particles such as electrons. The strength and direction of a magnetic field can be represented by field lines, with the direction of the field indicated by the direction of the lines and the strength indicated by the density of the lines.

How is a magnetic field created?

A magnetic field can be created in several ways. One way is through the movement of electric charges, such as in a current-carrying wire. Another way is through the alignment of intrinsic magnetic moments of particles, such as in a permanent magnet. Additionally, a changing electric field can also induce a magnetic field.

What is the difference between a magnetic field and an electric field?

A magnetic field is created by moving electric charges or intrinsic magnetic moments, while an electric field is created by stationary electric charges. In addition, an electric field exerts a force on other electric charges, while a magnetic field exerts a force on moving electric charges.

How does a magnetic field interact with other magnetic fields?

Magnetic fields can interact with each other in several ways. If two magnetic fields are parallel and in the same direction, they will attract each other. If they are parallel and in opposite directions, they will repel each other. If the fields are at an angle, they will exert a torque on each other, causing them to rotate. Additionally, a changing magnetic field can induce an electric field and vice versa.

What is the role of a magnetic field in electromagnetism?

A magnetic field plays a crucial role in electromagnetism, as it is responsible for the interaction between electric charges and the creation of electric currents. It is also a key component in many technological devices, such as motors, generators, and MRI machines. Understanding and controlling magnetic fields is essential for many fields of science and technology.

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