Magnetic Flux Formula

Magnetic flux formula

Magnetic flux refers to the total number of magnetic field lines passing through a given surface. Magnetic flux is represented by Φ_B and the unit is Weber (Wb).

Magnetic flux is the product of the average magnetic field and the perpendicular area through which it passes. The unit of magnetic flux is either Weber (Wb) or Tesla – meter². The magnetic field flux value could be a vector quantity depending upon the flux. The magnetic flux can be described mathematically as,

              Φ_B = BA cos θ

Here,

          Φ_B = Magnetic flux,

          B = Magnetic field force,

          A = Area of the surface through which flux passes.

          Θ = Angle between the surface and magnetic field line.

If a coil with n turns of area A, is placed in a magnetic field of strength B, then magnetic flux is given by,

Φ_B = nBA cos θ

Conditions for maximum and minimum magnetic flux

·        The magnetic flux obtained is maximum when the angle between the magnetic field line and the surface is 0˚.

According to the formula,

                 Φ_B = BAcos 0˚ = BA

·        The magnetic flux obtained is minimum when the angle between the magnetic field line and the surface is 90.

 According to the formula,

                 Φ_B = BAcos 90 = 0

Properties of magnetic flux

·        Magnetic flux always forms a closed loop.

·        Magnetic flux never intersects with one another.

·        Magnetic flux is a scalar quantity.

·        Magnetic flux starts from the north pole and ends at the south pole.

Solved examples

Example 1: A magnetic field of 8.9 T passes perpendicular to a disc with a radius of 5 cm. Find the magnetic flux of the disc.

Solution:

            Magnetic field is given by, B = 8.9 T,

             Radius is given by, r = 5 cm = 5 × 10^-5 m,

             As the magnetic field is perpendicular to the disc, θ = 0,

             Area is given by = π(5 x 10^-2)²

             Φ_B =?

By applying the formula,

             Φ_B = BAcos θ = 8.9 x π(5 x 10^-2)² x cos 0

                  = 139.7 x 10^-4 Wb.

Example 2: The dimensions of a square loop is 0.40m x 0.40m. B and θ are 0.05T and 60° respectively. Determine the magnetic flux.

Solution:

              B = 0.05 T,

              A = 0.4 x 0.4 = 0.16 m²,

              Θ = 60°

              Φ_B =?

By applying the formula,

              Φ_B = BAcos θ = 0.05 x 0.16 x cos 60°

                    = 0.004 Wb.