Final answer:
The direction of the electric field at point P is vertical to the plane of charges, due to the symmetry of the charge distribution. The magnetic field at a point on the +x-axis near a wire carrying current in the +y-direction points out of the page, according to the right-hand rule. Principles such as Gauss's law and the superposition principle assist in these determinations.
Step-by-step explanation:
The direction of the electric field at a point P located along the x-axis is determined by the symmetry of the charge distribution and the type of charge. If we consider a plane of charges that are symmetric with respect to point P, the components of the electric field parallel to the plane of charges will cancel out. Therefore, we conclude that the electric field at point P is directed vertically (perpendicular) from the plane of charges.
In the context of a wire carrying current along the y-axis, the right-hand rule can be used to determine the direction of the magnetic field at a point on the +x-axis near the wire. Since the current is flowing in the +y-direction, you would point your thumb in the direction of the current (+y) and curl your fingers. Your fingers would then point out of the page on the right side of the wire (+x-axis), indicating the direction of the magnetic field there.
When calculating the magnitude and direction of electric or magnetic fields, several principles come into play, including Gauss's law and the superposition principle. These principles, together with specific conditions such as the charge per unit length (λ) or the current (I) and distance from the wire (R), allow for the determination of the field's characteristics at a given point P.