Question

We must find a location farther away from the wire carrying the larger current and closer to the wire carrying the smaller current, where the fields created separately by the currents are equal in magnitude but opposite in direction. We will compute the magnitude and identify the direction of the magnetic field each current creates at the location between them. We will add the fields as vectors and find the magnetic force on the moving charge from a cross product. In the last part of the problem, we will review the definition of the electric field by finding an electric field whose force counterbalances the force on the moving charge so that the charge moves undeflected through the fields.

Analyze above the pair of wires, the field out of the page of the I2.

Answer 1

This question explores the physics of magnetic fields and forces between parallel current-carrying wires, based on the right-hand rule and the magnetic interaction between the wires.

Step-by-step explanation:

The subject in question relates to the principles of electromagnetism, specifically the interaction of magnetic fields created by electric currents in long straight parallel conductors. By applying the right-hand rule, we can determine the direction of these magnetic fields as well as the forces exerted on charge-carrying wires placed within these fields. The force between two conductors carrying currents in opposite directions can be analyzed through their created magnetic fields. The resulting force on a wire is given by the product of the magnetic field and the current in the wire, with direction determined by the right-hand rule.

In cases where the currents in wires run in opposite directions, the magnetic fields between the wires reinforce each other, while outside, the fields tend to cancel out. By calculating these fields and forces, one can also find a point where the magnetic fields created by each wire are equal in magnitude but opposite in direction. At this point, a charged particle would experience no net magnetic force, allowing us to explore equilibrium situations where electric fields may counterbalance the magnetic forces, leaving the charged particle moving undeflected.

This analysis is crucial in understanding the behavior of currents in parallel wires and their magnetic interaction, which has practical applications in engineering and technology, including the design of electrical circuits and components.