Two long straight wires are parallel and 8.0 cm apart. They are to carry equal currents such th

step 1 Hi, in the given problem, there are two straight parallel current carrying conductors. They are

Two long straight wires are parallel and 8.0 cm apart. They...

Two long straight wires are parallel and $8.0 \mathrm{~cm}$ apart. They are to carry equal currents such that the magnetic field at a point halfway between them has magnitude $300 \mu \mathrm{T}$. (a) Should the currents be in the same or opposite directions? (b) How much current is needed?

Key Concepts

Effect of Current Directions on Field Contribution

The directions in which currents flow in nearby conductors greatly influence the resulting magnetic field due to the additive or subtractive qualities of their field vectors. In configurations where the fields at a point must add constructively, appropriate current orientations—such as opposite directions in certain symmetric setups—are necessary to achieve the desired net magnetic field.

Right-Hand Rule for Magnetic Fields

The right-hand rule is used to determine the direction of the magnetic field around a current-carrying wire. By aligning the thumb in the direction of the current flow, the curled fingers show the orientation of the field lines. This rule is crucial for analyzing the relative directions of fields produced by multiple conductors.

Magnetic Field Due to a Long Straight Conductor

This concept involves calculating the magnetic field produced by a long straight wire carrying a current, using the formula B = (??I)/(2?r). Here, ?? is the permeability of free space, I is the current, and r is the distance from the wire. It is a primary tool in magnetism to estimate the influence of electric currents on the surrounding space.

Superposition Principle in Magnetism

The superposition principle states that the net magnetic field at any point is the vector sum of the magnetic fields produced by each current-carrying element independently. This concept is fundamental when considering systems with multiple wires, where each wire's contribution is calculated separately and then added together to determine the overall field at a specific location.

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