Final answer:
The magnetic force on a wire carrying current in a magnetic field is perpendicular to both the current and the magnetic field, determined by the right-hand-rule. The magnetic field around a wire is circular and the force depends on the orientation of the current. Complex magnetic field scenarios require the integral form of the magnetic force equation.
Step-by-step explanation:
Magnetic Force on a Wire
When a wire carrying a current I is placed in a magnetic field B, it experiences a magnetic force F given by the right-hand-rule, which is F = I * L * B * sin(θ) where L is the length of the wire within the magnetic field and θ is the angle between the current's direction and the magnetic field. The direction of the force is perpendicular to both the current and the magnetic field.
For a wire along the y-axis with current in the +y-direction, the magnetic field at a point on the +x-axis would be circular around the wire, as per the right-hand thumb rule, which means the magnetic field would point in the +z or -z direction (out of the plane or into the plane) at that point on the +x-axis.
In the case of a wire exposed to Earth's magnetic field, which has both horizontal and vertical components, the magnetic force on the wire would again depend on the direction of the current with respect to the magnetic field orientation, and can be determined using the right-hand-rule.
When calculating the force between two parallel wires or the force on a wire within a complex magnetic field, one can use the integral form of the magnetic force equation F = ∫ (I dL × B), considering the vector nature of the force, current, and magnetic field with the cross-product.