Magnets and Magnetic Field

Definition: A magnet is an object that attracts iron, possessing two distinct ends known as the north pole and south pole.
Functionality: The attraction towards iron is due to the electrons of the atoms in a magnet all spinning in one direction, producing a magnetic force.

Definition: A magnetic field is a region surrounding a magnet where magnetic forces can be detected.
Strength Indicators: The magnetic field is strongest at the poles of the magnet. At the north and south poles, the magnetic field lines are closest together, indicating higher strength.
Drawing Magnetic Fields: When representing a magnetic field, it is important to draw curved lines emanating from the north pole to the south pole, with density of lines indicating strength. These lines are referred to as:
  - Magnetic field lines
  - Flux lines
  - Lines of force

Definition: A compass itself is a magnet, with its north pole attracted to the south pole of another magnet.
Earth's Magnetism: The north pole of a compass is attracted to the south pole of Earth's magnetic field.
Property of Magnetic Flux: Magnetic flux lines are always directed from the north pole to the south pole and they never cross.

Maximal Strength: The magnetic field becomes stronger when the magnetic field lines are closer together.
Measurement of Magnetic Field Strength: Magnetic field strength, or magnetic flux density, is defined by the number of lines of flux per unit area. The standardized unit for magnetic flux is the weber (Wb).
Mathematical Representation: Magnetic induction is denoted by the letter B, with the formal SI unit being $ext{Wb/m}^2$ , which is also known as the tesla (T). Magnetic induction is a vector quantity.

Concept: It was found that a wire carrying an electric current produces a magnetic field around it.
Magnetic Field Direction: The magnetic field generated by a current-carrying wire is circular, with the plane of the field being perpendicular to the direction of the electric current.
Right Hand Rule: To determine the direction of the magnetic field, one can use the right-hand rule where:
- The right hand indicates conventional current (proton direction).
- For electron flow, the left hand should be used.
Dots and X's Representation: In two-dimensional representation, dots are used for fields exiting the plane (out of the screen), and X's for fields entering the plane (into the screen).

Definition: Electromagnetic induction occurs when a wire cuts through magnetic field lines, causing an electromotive force (emf) that results in charge movement and establishes potential difference across the wire.
Effect on Magnetic Fields: When the wire moves through the magnetic field, one end becomes negatively charged while the other end becomes positively charged.
Influence of Motion: The potential difference is greatest when the wire moves perpendicularly to the magnetic field direction and the wire’s length. Conversely, the potential difference is minimal when the wire moves parallel to the field lines.

Relationship for Force: When a current-carrying wire is aligned perpendicularly to a magnetic field, the force on the wire can be found using the equation:
   $F = I imes B$
  - Where:
    - $F$ = Force (Newtons, N)
    - $I$ = Current (amperes, A)
    - $B$ = Magnetic field (tesla, T)
Scenario Example: In a magnetic field of strength $3.0 imes 10^{-3}$ T, with a current of $100$ A and length of $2$ m, the force can be calculated according to the above relationship.
Right Hand Rule #3: This rule is employed to determine the direction of the force on the wire, where:
  - Thumb points in the direction of conventional current (I).
  - Fingers point in the direction of the magnetic field (B).
  - Palm indicates the direction of the resultant force (F).

General Principle: The potential difference increases when a wire moves faster across a magnetic field or cuts through more field lines, leading to higher induced emf. Therefore, the location of field lines influences the induced potential difference.
Circuit Formation: When additional wires connect to the original wire, a circuit is formed allowing the potential difference in the wire to drive current flow. This current can power electrical devices, such as light bulbs.

Mechanism: When an electric current passes through a wire, a magnetic field is generated around the wire.
Enhancing Strength: If the wire is shaped into a coil and an iron core is inserted, the iron becomes a stronger magnet—provided an electric current flows through the wire.