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: