F=qvB: Questions about Charge & Velocity

[kelvin490]

In applying F=qvB, must the charge move with velocity V? Or the V is only relative velocity so that even the charge is stationary but the magnetic field is moving the same result (force) can be achieve?

 

[Borg]

Think about the difference between a motor and a generator. How would you describe the forces involved?

 

[Naty1]

yes, all velocities are relative. Relative motion produces the force...

 

[Bob_for_short]

In applying F=qvB, must the charge move with velocity V? Or the V is only relative velocity so that even the charge is stationary but the magnetic field is moving the same result (force) can be achieve?

In any reference frame a charge q has a velocity v. The force due to the magnetic filed is qvxB. This is a part of the Newton equations. The magnetic filed B can be space-time dependent or constant, whatever. But if the charge velocity is equal to zero, no magnetic force is possible: this term equals zero. Only electric qE, elastic kx, etc., may still act. To keep a charge at rest, all forces should cancel in the Newton equations. Otherwise it will move under qE, for example.

 

[kelvin490]

In any reference frame a charge q has a velocity v. The force due to the magnetic filed is qvxB. This is a part of the Newton equations. The magnetic filed B can be space-time dependent or constant, whatever. But if the charge velocity is equal to zero, no magnetic force is possible: this term equals zero. Only electric qE, elastic kx, etc., may still act. To keep a charge at rest, all forces should cancel in the Newton equations. Otherwise it will move under qE, for example.

thanks.

What if we have a reference frame that the charge is at rest, but a magnet is move close to it? Will it experience a force and be moved?

 

[Bob_for_short]

...What if we have a reference frame that the charge is at rest, but a magnet is move close to it? Will it experience a force and be moved?

Yes, it will. A moving magnet, apart from magnetic field creates an electrical field E determined with the magnet velocity, so the total force will be non-zero.

The value of electrical filed E can be calculated from the Lorentz transformations for fields. In the non relativistic approximation it will be E ∝ VxB where V is the magnet velocity.