The maximum flux density in a transformer core can be calculated using the following formula:
max
=
rms
×
1
0
8
4.44
×
×
core
×
B
max
=
4.44×f×A
core
×N
V
rms
×10
8
Where:
max
B
max
is the maximum flux density in Tesla (T) or Weber per square meter (Wb/m²).
rms
V
rms
is the root mean square (RMS) voltage applied to the transformer primary coil in volts (V).
f is the frequency of the alternating current (AC) in Hertz (Hz).
core
A
core
is the cross-sectional area of the transformer core in square meters (m²).
N is the number of turns in the primary winding of the transformer.
This formula is derived from Faraday's law of electromagnetic induction, which relates the induced electromotive force (EMF) in a coil to the rate of change of magnetic flux through the coil. The maximum flux density occurs when the core is fully saturated, and exceeding this value could lead to magnetic core saturation and increased losses in the transformer. It's essential to design transformers with appropriate core materials and dimensions to ensure the maximum flux density remains within safe operating limits.