Need help for a prove about magnetic field and magnetic force

In summary, the problem is to prove that the vector of the magnetic force cannot be parallel to the plane containing the particle's velocity and magnetic field. It is difficult to prove this without using the definition of the cross product, as the behavior of charged particles interacting with a magnetic field is observed rather than derived.
  • #1
humanallien
2
0
here is the problem:

prove that the vector of the magnetic force cannot be parallel to the plane that contains the vector of the particle's velocity and magnetic field.

someone please help me to solve this, thanks so much for your time.
 
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  • #2
humanallien said:
here is the problem:

prove that the vector of the magnetic force cannot be parallel to the plane that contains the vector of the particle's velocity and magnetic field.

someone please help me to solve this, thanks so much for your time.

By definition of cross product you have both

[tex]\vec v \cdot \vec v \times \vec B = 0[/tex]

and

[tex]\vec B \cdot \vec v \times \vec B = 0[/tex]

which say that both [itex]\vec v[/itex] and [itex]\vec B[/itex] are perpendicular to [itex]\vec F = \vec v \times \vec B[/itex].
 
  • #3
thanks for your advice, but it does not help me with the problem because I have to assume that I do not know the definition of F = v X B for the prove. Therefore, I want to proof that the force vector is NOT parallel to the plane without considering the definition of the croos product
 
  • #4
Since the fundamental behavior of charged particles interacting with a magnetic field comes only from observation (Thomson, Lorentz, etc.) it would seem unlikely that you could "prove" the result by other means. It would be like attempting to prove the electric force on a charged particle acts parallel to the electric field - without invoking Coulomb's Law. Good luck!
 

1. What is a magnetic field?

A magnetic field is a region in space where magnetic forces can be detected. It is created by moving electric charges, such as the flow of electrons in a wire, or by magnetic materials, such as magnets.

2. How is a magnetic field created?

A magnetic field is created by moving electric charges or by magnetic materials. When an electric current flows through a wire, it creates a circular magnetic field around the wire. In magnets, the alignment of the atoms' magnetic fields creates a larger magnetic field.

3. What is the relationship between magnetic field and magnetic force?

Magnetic force is the force exerted by a magnetic field on a moving electric charge or a magnetic material. The strength of the magnetic force depends on the strength of the magnetic field and the velocity of the charge or material.

4. How can we measure the strength of a magnetic field?

The strength of a magnetic field can be measured using a device called a magnetometer, which detects the force exerted by the magnetic field on a test charge. The unit of measurement for magnetic field strength is the tesla (T) or the gauss (G).

5. What are some real-life applications of magnetic fields and magnetic force?

Magnetic fields and magnetic force have many practical applications in everyday life. Some examples include electric motors, generators, MRI machines, speakers, and magnetic levitation trains. They are also used in compasses and magnetic storage devices such as hard drives.

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