Talha's Physics Academy
Electromagnetism - Magnetic Flux and Flux Density
Q. Explain the term magnetic flux and magnetic flux density.
Magnetic Flux
"The total number of magnetic lines of induction passing normally through a given surface is called magnetic flux."
The magnetic flux ($\Delta\Phi_m$) depends upon the following factors:
- Magnetic field of induction ($B$): The stronger the magnetic field, the greater will be the flux passing through the surface:
$\Delta\Phi_m \propto B$
- Area of the surface ($\Delta A$): The greater the surface area, the more magnetic field lines will pass through it:
$\Delta\Phi_m \propto \Delta A$
- Cosine of the angle ($\theta$) between $\vec{B}$ and $\Delta\vec{A}$: The orientation of the surface relative to the field lines determines how many lines pass through:
$\Delta\Phi_m \propto \cos\theta$
By combining these factors, we get:
$\Delta\Phi_m = B \Delta A \cos\theta \quad \text{--- (1)}$
Vectorially, magnetic flux is expressed as the dot product of the magnetic field vector and the area vector:
$\Delta\Phi_m = \vec{B} \cdot \Delta\vec{A}$
Its SI unit is the Weber ($\text{Wb}$).
Special Cases for Magnetic Flux
- (a) When $\theta = 0^\circ$: The surface is perpendicular to the magnetic field lines (area vector is parallel to the field):
$\Delta\Phi_m = B \Delta A \cos(0^\circ) = B \Delta A \times 1 = B \Delta A \quad \text{(Maximum Flux)}$
- (b) When $\theta = 90^\circ$: The surface is parallel to the magnetic field lines (area vector is perpendicular to the field):
$\Delta\Phi_m = B \Delta A \cos(90^\circ) = B \Delta A \times 0 = 0 \quad \text{(Zero Flux)}$
Magnetic Flux Density
"Magnetic flux per unit area passing normally through a surface is called magnetic flux density ($B$)."
Mathematically, flux density is defined as:
$B = \frac{\Delta\Phi_m}{\Delta A}$
Its SI unit is Weber per square meter ($\text{Wb/m}^2$), which is commonly known as the Tesla ($\text{T}$).
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