Effect of a current carrying wire on a point charge 
Given a point charge $q$ near a wire carrying current as shown, what would be the effect of the magnetic field produced by the wire on this point charge $q$? I think the sign on $q$ is important so let's consider both cases in which the charge $q$ is positive and negative separately.
 A: Use the right-hand rule: the thumb goes upwards with the conventional current of the wire. This means the magnetic field will be going counter-clockwise when viewed from the top.
At the location of the charge, the magnetic field points out of the screen. Now, use Fleming's left-hand rule: The thumb will be the direction of the force which we want, the index finger is the magnetic field (out of the screen), and the middle finger is the movement of the charge, however, the charge is not moving! So no force!
Mathematically, this is seen as: $\vec{F}=q\vec{v}\times\vec{B}$. Since the charge is not moving, $\vec{v}=0$, and thus $\vec{F}=0$. Since no force is acting on the stationary charge there will be no acceleration and no movement.
Note: the only difference between a positive and negative charge in relation to this would be the direction of the charge's movement in the left-hand rule. If it is positive, then it is the normal direction. If negative, then it is opposite to the direction. This is because of the definition of conventional current used in such rules.
