Magnetic Flux

Magnetic Flux (Φ_B)

The magnetic flux through an area A in a magnetic field is defined as the number of magnetic field lines passing through that area normally and is given by the equation (Figure 4.1(a)).

where the integral is taken over the area A and θ is the angle between the direction of the magnetic field and the outward normal to the area.

If the magnetic field  is uniform over the area A and is perpendicular to the area as shown in Figure 4.1(b), then the above equation becomes

The SI unit of magnetic flux is T m². It is also measured in weber or Wb.

1 Wb = 1 T m²

EXAMPLE 4.1

A circular antenna of area 3 m² is installed at a place in Madurai. The plane of the area of antenna is inclined at 47º with the direction of Earth’s magnetic field. If the magnitude of Earth’s field at that place is 40773.9 nT find the magnetic flux linked with the antenna.

Solution

B = 40773.9 nT; θ = 90º  – 47º  = 43°;

A = 3m²

We know that  Φ_B = BAcosθ

EXAMPLE 4.2

A circular loop of area 5 x 10^-2m² rotates in a uniform magnetic field of 0.2 T. If the loop rotates about its diameter which is perpendicular to the magnetic field as shown in figure. Find the magnetic flux linked with the loop when its plane is (i) normal to the field (ii) inclined 60o to the field and (iii) parallel to the field.

Solution

A = 5 ´ 10^-2 m²; B = 0.2 T

(i) θ = 0°