A standard door into a house rotates about a vertical axis through one side, as defined by the door's hinges. A uniform magnetic field is parallel to the ground and perpendicular to this axis. Through what angle must the door rotate so that the magnetic flux that passes through it decreases from its maximum value to 0.30 of its maximum value?

The angle that the door must rotate is 70.5 graus

Explanation:

When the door rotates through and angel X, the magnetic flux that passes through the door decreases from its maximum value to 0.3 of its maximum value

This way,

X = 0.3 Xmax

X = B A cosX = 0.3 B A  

or

cosX = 0.3

or

X = (0.3) = 70.5

X = 70.5 graus

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