Magnets Help pleaseeee?

Question

A horizontal magnetic field B points east, perpendicular to the horizontal component Be of the earth's magnetic field.

a) If the ratio B/Be = square root (3), in which direction (angle) will the compass needle point? (Assume that the compass needle rotates in the horizontal plane and Be points north).

b) If the compass needle points exactly northwest, what is the magnitude of B?

Answer 1

Magnetic fields just add like vectors so:

a) B = sqrt(3) * Be so the vector would be ( sqrt(3) * Be, Be)  = ( x, y)  assuming positive y is North and positive x is East then the ArcTan( y/x) = ArcTan( 1/sqrt(3)) = 30 degrees.

b) If the needle points northwest then B must be the same magnitude as Be, however it points West not East so if the East direction is positive then B = -Be