[Gucki]

Depends the magnetic force on the velocity of charges in a conductor?



Yes, the magnetic force on a moving charge in a conductor depends on the velocity of the charge. The relationship is given by the Lorentz force equation, which describes the force on a charged particle moving through a magnetic field:

\[
\mathbf{F} = q (\mathbf{v} \times \mathbf{B})
\]

Where:
- \( \mathbf{F} \) is the magnetic force on the charge,
- \( q \) is the charge of the particle,
- \( \mathbf{v} \) is the velocity of the charged particle,
- \( \mathbf{B} \) is the magnetic field, and
- \( \times \) represents the vector cross product.

### Key points about the dependence on velocity:

1. **Magnitude of the Force**: 
   The magnitude of the magnetic force is proportional to the speed of the charged particle. Specifically, it is proportional to \( v \), the magnitude of the velocity:
   \[
   |\mathbf{F}| = |q| v B \sin(\theta)
   \]
   where \( \theta \) is the angle between the velocity vector \( \mathbf{v} \) and the magnetic field vector \( \mathbf{B} \).

2. **Direction of the Force**: 
   The direction of the force depends on the direction of the velocity relative to the magnetic field. The force is always perpendicular to both the velocity of the charge and the magnetic field, as determined by the right-hand rule for the cross product.

3. **Velocity's Role in Current**: 
   In a conductor carrying a current, the velocity of the charge carriers (electrons, typically) plays a critical role in determining the magnetic force on each charge. If the velocity increases, the magnetic force on each individual charge increases, which can also affect the overall behavior of the current in the conductor (such as the induced voltage or the generation of secondary magnetic fields, as described by Ampère's Law).

In short, the magnetic force is directly proportional to the velocity of the charge. The faster the charge moves, the greater the force exerted on it by the magnetic field, assuming all other factors (like charge and magnetic field strength) are constant.