Problem 4: a long wire carries current towards east. a positive charge moves westward and just north from the wire. what is the direction of the force experienced by this charge?

The direction of the force experienced by the positive charge is upward.

We can use the right-hand rule to understand the direction of the Lorentz force acting on the charge: let's put the thumb in the same direction of the current in the wire (eastward), while the other fingers "wrap themselves" around the wire. These other fingers give the direction of the Lorentz force in every point of the space around the wire. Since the charge is located north of the wire, in that point the fingers are directed upward, so the positive charge experiences a force directed upward.
(if it was a negative charge, we should have taken the opposite direction)

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