B y: E n g r. H i n e s h Ku m a r ( Le c t u re r )

MAGNETIC FLUX & MAGNETIC FLUX DENSITY

Definition• Magnetic flux (most often denoted as Φ).

The number of magnetic (flux) field lines which pass through a given cross-sectional area A.• The SI unit of magnetic flux is the weber (in

derived units: volt-seconds). • The CGS unit is the Maxwell.

Explanation• Consider an area ‘A’, placed in a magnetic

field. • Let this area is divided into small segments each of  area DA.• Flux through DA is the product of area and the normal component of field B, i.e ACosBAB )(

ABOR

ABCos

DD

DD

.

Cont…• A = area of loop• Φ= angle between B and the normal to the

loop• Now flux over whole area A is the sum of

fluxes through all elements ∆A i.e.

ABOR

ABABAB

D

DDDDDD

.

...............

332211

321

Problem #1 Magnetic Flux• A rectangular coil of wire is situated in a

constant magnetic field whose magnitude is 0.50 T. The coil has an area of 2.0 m2 . Determine the magnetic flux for the three orientations, f = 0°, 60.0°, and 90.0°, shown below.

Magnetic Flux Density• It is defined as the amount of magnetic flux in

an unit area perpendicular to the direction of magnetic flow.• The Magnetic Flux Density (B) is related to

the Magnetic Field (H) by:

• μ is the permeability of the medium (material) where we are measuring the fields.

HB

Cont…• The magnetic flux density is measured in

Webers per square meter [Wb/m^2], which is equivalent to Teslas [T]. • The B field is a vector field, which means it

has a magnitude and direction at each point in space.• The constant μ is not dimensionless and has

the defined value for free space, in henrys per meter (H/m), of

mH /104 7