12.11 Magnetic Flux | Electromagnetism | Physics 11

Magnetic flux refers to the total magnetic field that passes through a specific area. The magnitude of the flux depends on the strength of the magnetic field, the area it passes through, and the angle between the field and the area vector.

Definition and Formula

Magnetic flux, symbolized as $Φ_{B}$ , is a measure of the quantity of magnetism. It is defined as the scalar product (dot product) of the magnetic field vector ( $B$ ) and the area vector ( $A$ ).

The formula is expressed as: $Φ_{B} = B \cdot A$

When the angle $θ$ between the magnetic field and the vector normal (perpendicular) to the area is known, the formula becomes:

$Φ_{B} = B A cos θ$

$B$ : The magnitude of the magnetic field strength.
$A$ : The area through which the magnetic field lines pass.
$θ$ : The angle between the magnetic field vector and the area vector (normal to the surface).

Scalar And Vector Quantities→

Units of Magnetic Flux

The standard unit for magnetic flux is the weber (Wb).

Quantity	Symbol	Unit	SI Equivalent
Magnetic Flux	$Φ_{B}$	weber	Wb ( $kg \cdot m^{2} \cdot s^{- 2} \cdot A^{- 1}$ )
Magnetic Field Strength	$B$	Wb/m²	tesla (T)
Area	$A$	m²	m²

Note: $1 Wb = 1 T \cdot m^{2} = 1 V \cdot s$

Derived Units→

Special Cases of Magnetic Flux

Maximum Flux: Flux is at its maximum when the surface is held perpendicular to the magnetic field lines. In this orientation, the angle $θ$ (between $B$ and the normal to the area) is $0^{\circ}$ , and $cos (0^{\circ}) = 1$ . $Φ_{B} = B A$
Minimum Flux: Flux is zero when the surface is parallel to the magnetic field lines. Here, the angle $θ$ is $9 0^{\circ}$ , and $cos (9 0^{\circ}) = 0$ . $Φ_{B} = 0$

Flux in Non-Uniform Fields or Curved Surfaces

To calculate the magnetic flux through a curved surface or within a non-uniform magnetic field, the surface is divided into small elements. The total flux is the sum of the flux through each individual element.

$Φ_{B} = \sum B \cdot Δ A$

Magnetic Flux Density

Magnetic flux density ( $B$ ), also known as magnetic induction, is the amount of magnetic flux per unit area passing through a surface perpendicular to the field.

$B = \frac{Φ}{A}$

The unit for magnetic flux density is Wb/m², which is equivalent to the Tesla (T).

Magnetic flux is a critical concept in electromagnetism, forming the basis for the operation of essential technologies like electric motors and transformers.

Definition and Formula

Magnetic flux, symbolized as

Φ_{B}

, is a measure of the quantity of magnetism. It is defined as the scalar product (dot product) of the magnetic field vector (

B

) and the area vector (

A

The formula is expressed as:

Φ_{B} = B \cdot A

When the angle

θ

between the magnetic field and the vector normal (perpendicular) to the area is known, the formula becomes:

Φ_{B} = B A cos θ

$B$ : The magnitude of the magnetic field strength.

$A$ : The area through which the magnetic field lines pass.

$θ$ : The angle between the magnetic field vector and the area vector (normal to the surface).

Quantity

Symbol

Unit

SI Equivalent

Magnetic Flux

Φ_{B}

weber

Wb (

kg \cdot m^{2} \cdot s^{- 2} \cdot A^{- 1}

)

Magnetic Field Strength

B

Wb/m²

tesla (T)

Area

A

m²

Special Cases of Magnetic Flux

Maximum Flux: Flux is at its maximum when the surface is held perpendicular to the magnetic field lines. In this orientation, the angle $θ$ (between $B$ and the normal to the area) is $0^{\circ}$ , and $cos (0^{\circ}) = 1$ . $Φ_{B} = B A$

Minimum Flux: Flux is zero when the surface is parallel to the magnetic field lines. Here, the angle $θ$ is $9 0^{\circ}$ , and $cos (9 0^{\circ}) = 0$ . $Φ_{B} = 0$

Magnetic Flux Density

Magnetic flux density (

B

), also known as magnetic induction, is the amount of magnetic flux per unit area passing through a surface perpendicular to the field.

B = \frac{Φ}{A}

The unit for magnetic flux density is Wb/m², which is equivalent to the Tesla (T).

Magnetic flux is a critical concept in electromagnetism, forming the basis for the operation of essential technologies like electric motors and transformers.