What is the difference between magnetic flux and magnetic flux density?

Short Answer:

Magnetic flux is the total amount of magnetic field passing through a given surface. It shows how much magnetic field is spread over an area and is measured in webers (Wb). Magnetic flux tells us the quantity of magnetic lines crossing through a surface like a coil or loop.

Magnetic flux density, on the other hand, is the amount of magnetic flux per unit area. It tells us how concentrated the magnetic field is over that area. It is measured in tesla (T). While magnetic flux gives the total field, magnetic flux density gives the field strength at a particular place.

Detailed Explanation:

Magnetic flux and magnetic flux density

In magnetism, it is important to understand how magnetic fields behave and how they are measured. Two closely related terms are magnetic flux and magnetic flux density. Although they are connected, they have different meanings and are used in different situations.

Magnetic flux

Magnetic flux is a measure of the total magnetic field that passes through a given surface. It shows how much magnetic field is flowing through a loop, coil, or any flat surface. Magnetic flux depends on three factors:

  1. Strength of the magnetic field (B)
  2. Area of the surface (A)
  3. Angle (θ) between the field and the surface

The formula for magnetic flux is:

ϕ=B⋅A⋅cos⁡θ\phi = B \cdot A \cdot \cos\thetaϕ=B⋅A⋅cosθ

Where:

  • ϕ\phiϕ = magnetic flux (in webers, Wb)
  • BBB = magnetic flux density (in tesla, T)
  • AAA = area through which field passes (in m²)
  • θ\thetaθ = angle between magnetic field and normal to the surface

If the field is perpendicular to the surface, the flux is maximum. If it is parallel, the flux is zero.

Magnetic flux density

Magnetic flux density refers to the amount of magnetic flux per unit area. It gives us an idea of how strong or concentrated the magnetic field is at a specific place. It is a vector quantity, meaning it has both direction and magnitude.

The formula for magnetic flux density is:

B=ϕAB = \frac{\phi}{A}B=Aϕ​

Where:

  • BBB = magnetic flux density (tesla, T)
  • ϕ\phiϕ = magnetic flux (weber, Wb)
  • AAA = area (m²)

A higher value of magnetic flux density means that the magnetic field is strong and tightly packed in that area.

Key differences

  1. Definition:
    • Magnetic flux is the total magnetic field passing through an area.
    • Magnetic flux density is the magnetic field per unit area.
  2. Symbol:
    • Magnetic flux: ϕ\phiϕ
    • Magnetic flux density: BBB
  3. Unit:
    • Magnetic flux: weber (Wb)
    • Magnetic flux density: tesla (T)
      (1 T = 1 Wb/m²)
  4. Dependence:
    • Flux depends on both area and magnetic field.
    • Flux density is independent of area; it’s field strength.

Real-life example

Imagine magnetic field lines passing through a metal loop.

  • Magnetic flux tells how many total field lines pass through the loop.
  • Magnetic flux density tells how closely packed those lines are in a particular part of the loop.

If the same number of field lines passes through a larger area, the flux density is lower. If they pass through a small area, the density is higher.

Conclusion:

Magnetic flux is the total magnetic field passing through a surface, measured in webers, while magnetic flux density is the strength of that magnetic field per unit area, measured in tesla. Flux gives the total effect, and flux density gives the intensity. Both are important in understanding and calculating magnetic effects in coils, motors, transformers, and other electrical devices.