The product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density

The magnetic flux is maximum when the magnetic field lines and the area they are travelling through are perpendicular
Φ =?BA
An aluminium window frame has a width of 40?cm and length of 73 cm shown in the diagram below.
The frame is hinged along the vertical edge AC.When the window is closed, the frame is normal to the Earth's magnetic field with magnetic flux density 1.8 × 10-5?T.
a) Calculate the magnetic flux through the window when it is closed.
b) Sketch the graph of the magnetic flux against angle between the field lines and the normal when the window is opened and rotated by 180°
Part (a)
Step 1: Write out the known quantities
Cross-sectional area,?A?= 40 cm × 73 cm = (40 × 10-2) × (73 × 10-2) = 0.292 m2
Magnetic flux density,?B?= 1.8 × 10-5?T
Step 2:?Write down the equation for magnetic flux
Φ =?BA
Step 3: Substitute in values
Φ = (1.8 × 10-5) × 0.292 = 5.256 × 10-6?= 5.3 × 10-6?Wb
Part (b)
The magnetic flux will be at a minimum when the window is opened by 90o?and a maximum when fully closed or opened to 180o

Consider carefully the value of θ, it is the angle between the field lines and the line?normal?(perpendicular) to the plane of the area the field lines are passing through. If it helps, drawing the normal on the area provided will help visualise the correct angle.
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