# Why does magnetism occur by moving charges

## Lorentz force

• Magnetism, magnetic fields, Lorentz force (8:52 minutes)
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### general definition

The Lorentz force is the force that a magnetic field on a moving cargo exercises. It is named after the Dutch mathematician and physicist Hendrik Antoon Lorentz.

\$\$ F = q \ cdot v \ cdot B \$\$ \ (q \) = charge, \ (v \) = speed, \ (B \) = magnetic flux density

### Direction of the Lorentz force

The Lorentz force acts on a moving charge in a magnetic field ...

... perpendicular to the direction of movement of the load

... perpendicular to the magnetic field lines

The figure on the left shows how to determine the direction of the force on a negative Charge with the help of the Left-hand rule can determine. Hold the thumb, index finger and middle finger of the left hand perpendicular to each other. The following then applies:

Thumb = direction of movement of the load (\ (v \))

Index finger = direction of the magnetic field lines (\ (B \))

Middle finger = direction of force (\ (F \))

The power to one positive Charge acts in exactly the opposite direction as it does on a negative charge. Therefore, for these charges, the same rules can be applied to the right hand to get the direction of the Lorentz force.

### Orbit shape of charges in magnetic fields

Charges move in magnetic fields Circular paths. This is because the Lorentz force acts perpendicular to the direction of movement of a charge. It therefore only changes the direction of the charge, but not its speed.

The figure on the left shows the orbit of a negative charge in the magnetic field.

The Lorentz force thus acts as a centripetal force. The following therefore applies:

\ begin {aligned} F_ \ mathrm {L} & = F_ \ mathrm {Z} \ q \ cdot \ cancel v \ cdot B & = \ dfrac {m \ cdot v ^ {\ cancel 2}} {r} \ \ q \ cdot B & = \ dfrac {m \ cdot v} {r} \ \ end {aligned}

### Simulation of the tracks

The following simulation shows the movement of charged particles in a magnetic field.

Adding particles with q = \ (-2 \, e \) \ (-e \) \ (0 \) \ (e \) \ (2 \, e \) \ (B = \) -1 \ (T \ )
Comparison: Charge Charge II Speed ​​Speed ​​II General: Empty