Question

What does the direction of the magnetic field depend on

Answer 1

in the case of a wire wound cylindrical solenoid .... which way the axis of the coil is pointing, I guess. So, if it's pointing towards the door, that's the field direction. Towards the window means that that's the direction.
I don't understand the q.
http://perendis.webs.com

Answer 2

IMHO,

F= ma, m is scalar variable, F & a is vector (scalar + direction) variable.
Thus : direction for force, F, is depending to the direction of acceleration, a.

For magnetic field of permanent magnets, B, it is flowing from North to South of a magnet.

For magnetic field of electromagnet, or magnets created by electrical current,then the relation is :
\[F = I.L \times B \]
where : F = force applied on wire, I = electrical current, L = length of the wire, B = magnetic field.

This is a vector cross product. Recall x, y, z plane. Draw it. :D
x cross y = z (note the direction)

same here -> (direction of F) = (direction of I).L x (direction of B)
where I, F, B = vector, L = scalar.

same as in this drawing. (:



hope that helps.

ref :
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html#c1
https://en.wikipedia.org/wiki/Fleming%27s_left-hand_rule_for_motors
http://members.tripod.com/Paul_Kirby/vector/Vcrossproduct.html