Study Notes on Electric Field (E) and Magnetic Field (B)

Concepts of Electric Field (E) and Magnetic Field (B)

Electric Field (E)

• Definition: The electric field (E) is a vector field around charged particles that represents the force exerted per unit charge at any point in space. It is defined mathematically as:

  • $extbf{E} = \frac{ extbf{F}}{q}$
  • Where:
    • $extbf{E}$ = Electric field vector
    • $extbf{F}$ = Force experienced by a test charge
    • $q$ = Magnitude of the test charge

• Unit: The SI unit of electric field is volts per meter (V/m).

• Direction: The direction of the electric field vector is determined by the direction of the force it exerts on a positive test charge.

• Key Relationships:

  • Uniform electric fields have constant magnitude and direction, while non-uniform electric fields vary.
  • Electric fields can be represented graphically with field lines:
  • Direction of lines indicates the direction of E.
  • Density of lines indicates the strength of E (closer lines = stronger field).

Magnetic Field (B)

• Definition: The magnetic field (B) is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. It is defined mathematically by the magnetic force experienced by a moving charge:

  • $extbf{B} = \frac{ extbf{F}}{I extbf{L} imes extbf{v}}$
  • Where:
    • $extbf{B}$ = Magnetic field vector
    • $extbf{F}$ = Magnetic force experienced by the moving charge
    • $I$ = Current in the wire
    • $extbf{L}$ = Vector length of the wire segment in the field
    • $extbf{v}$ = Velocity of the charge

• Unit: The SI unit of magnetic field is tesla (T).

• Direction: The direction of the magnetic field is given by the right-hand rule; it is perpendicular to both the direction of current and the movement of the charge.

• Key Characteristics:

  • Magnetic field lines provide visualization:
  • Lines emerge from the north pole and enter the south pole of magnetic materials or solenoids.
  • The density of field lines indicates the strength of the magnetic field.

Interconnection between Electric Field and Magnetic Field

• Maxwell's Equations: Describe how electric and magnetic fields interact and propagate through space. They are fundamental to understanding classical electromagnetism.
• Electromagnetic Waves: Electric and magnetic fields oscillate at right angles to each other and the direction of wave propagation.
  • Relation: $c = \frac{1}{ ext{sqrt}( ext{μ}_0 ext{ε}_0)}$
  • Where:
    • $c$ = speed of light in a vacuum
    • $ext{μ}_0$ = permeability of free space
    • $ext{ε}_0$ = permittivity of free space.