Magnetic flux is maximum when the magnetic field lines are perpendicular to the surface area; in other words, when the angle between the magnetic field vector and the normal vector to the surface is 0°.
To understand this better, let's break down magnetic flux:
What is Magnetic Flux?
Magnetic flux (ΦB) is a measure of the amount of magnetic field lines passing through a given surface area. It's a scalar quantity, meaning it has magnitude but no direction.
The Formula
The magnetic flux is calculated using the following formula:
ΦB = B ⋅ A = BA cos θ
Where:
- ΦB is the magnetic flux (measured in Webers, Wb)
- B is the magnetic field strength (measured in Tesla, T)
- A is the area of the surface (measured in square meters, m2)
- θ is the angle between the magnetic field vector (B) and the normal vector to the surface area (A). The normal vector is a vector that is perpendicular to the surface.
Maximizing Magnetic Flux
From the formula, we can see that the magnetic flux is directly proportional to the cosine of the angle θ. The cosine function reaches its maximum value (1) when the angle is 0°.
Therefore:
- θ = 0°: cos(0°) = 1, so ΦB = BA (Maximum magnetic flux)
This means the magnetic flux is maximum when the magnetic field lines are perpendicular to the surface area. All the magnetic field lines pass directly through the surface.
Minimizing Magnetic Flux
Conversely, the magnetic flux is minimum (zero) when the angle is 90°.
- θ = 90°: cos(90°) = 0, so ΦB = 0 (Minimum magnetic flux)
In this case, the magnetic field lines are parallel to the surface and do not pass through it.
In Summary
Magnetic flux is maximized when the magnetic field lines pass perpendicularly through the surface, meaning the angle between the magnetic field vector and the normal vector of the surface is 0°. This results in all the magnetic field lines contributing to the flux.
