# Physics Speedrun - Magnetic Field Magnetic Field

Magnetism is the interaction of clectric currents or moving charges. Magnetic field is

1. Created by / interacts on currents or moving charges
2. Closed field lines without beginning or end

## Ampere Force

Magnetic field exerts a force on a current, called Ampere forece. In uniform field: Ampere force in uniform field

The magnetic field is defind by the formula . SI Unit for : Tesla

General case: nonuniform , curved wire: Curved wire in uniform field

In uniform field, it is equivalant to a stright wire from A to B. Interaction of currents

Magnetic field freated by current

### Magnetic Dipole A rectangular current loop in a uniform field

Total force is zero, but torque on the loop:

Magnetic dipole moment:

Direction of is defined by the right-hand rule.

Torque:

Valid for any plane current loop. A small circular current is called a magnetic dipole.

For a loops coil / solenoid: An electron in an atom

Orbital angular momentum: A rotating uniformly charged disk

### Lorentz Force

Magnetic field exerts a force on a moving charge:

Lorentz force does not do work on the charge.

When , , free motion. Uniform circular motion

When , the point charge do a uniform circular motion. General case

The charge moves in a helix.

Lorentz equation: Total force on a charge in electromagnet field The Hall effect

## Source of Magnetic Field

### Biot-Savart Law Infinitesimal current

Magnetic equivalant to Coulumb's law. Magnetic field due to an infinitesimal current:

Permeability of free space:

Direction: right-hand rule.

Total magnetic field due to a full current: A straight current

Infinite straight current: No magnetic field at A or B. Also no field inside the cylinder when all the current is on the surface. Force between parallel wires

per unit length: Circular current on the axis

Magnetic dipole moment: At the center of circular / arc current

### Gauss's Law for Magnetic Field

Magnetic flux:

Gauss's law for magnetic field: Magnetic field lines

Magnetic field lines are closed lines without beginning or end.

### Ampere's Law

Magnetic field is produced by all currents: The sign of enclosed current: right-hand rule

Magnetic field is not a conservative field:

Maxwell equations for steady magnetic field and electrostatic field: Proper integral path for calculating magnetic field of a cylinderical current Coaxial cable

No magnetic field when . Central part of solenoid

Uniform magnetic field inside: Follow the intergration path. Toroid

Nonuniform field inside: