Magnetic flux and Magnetic density

Question: Define mafnetic flux, maximum magnetic flux, minimum magnetic flux, magnetic flux through curved surface and give unit of magnetic flux and define flux density and give its unit?

MAGNETIC FLUX

The.dot product of uniform magnetic field Band vector area Ā of plane element is called magnetic flux. It is denoted by ΦB

ΦB = B . A

⇒ ΦB = BA Cos θ

Here A is a vector area of plane element whose direction is along the normal to the surface of the element and Ө is the angle between the directions of the vectors B and A.

MAXIMUM MAGNETIC FLUX

When magnetic field is directed along normal to surface area (A) and parallel to vector area (Ā), Ө is zero, and the flux is maximum.

ФB = B.A = BA Cos O°

= BA (1)

= BA (max.)

MINIMUM MGNETIC FLUX

When magnetic field B is perpendicular to vector area (Ā). Then Ө = 90° and the flux is minimum (Zero).

ΦB = B. A = BA Cos 90°

= BA (0)

= 0 (minimum).

MAGNETIC FLUX THROUGH CURYED SURFACE IN NON, UNIFORM MAGNETIC FIELD

When curved surface is placed in a uniform magnetic field, the curved surface is divided into a number of small surface elements each element assumed plane and the flux through the whole curved surface is calculated by taking sum of all contributions of the surface.

ΦB = BA = N / A x m ✖️ m²

NmA-1 = Wb (weber)

MAGNETIC FLUX DENSITY

Magnetic flux per unit area of a surface perpendicular too is called magnetic flux density. It is also called magnetic induction or magnetic field strength. It is denoted by B.

ΦB = BA

B = ΦB / A

UNIT

B = ΦB / A = Wb / m² = Wbm-²

NA-1m-1 or Tesla