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

step 1 For part A of the problem, the current must be opposite, opposite and anti -parallor, or anti -p

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$\mu$ (a) Should the
currents be in the same or opposite directions? (b) How much
current is needed?

Key Concepts

Magnetic Field of a Current-Carrying Wire

A long straight conductor carrying a steady current generates a magnetic field that forms concentric circles around the wire. The magnitude of this field is given by B = (?0 I) / (2?r), where I is the current, r is the distance from the wire, and ?0 is the permeability of free space. This concept is fundamental in electromagnetism and is derived from Ampère’s Law or the Biot–Savart Law.

Superposition Principle in Magnetic Fields

The superposition principle states that when multiple magnetic fields are present, the resultant field at any point is the vector sum of the individual fields. This means that in scenarios with several current-carrying wires, the net magnetic field is determined by adding the contributions from each wire, taking into account both their magnitudes and directions.

Right-Hand Rule for Magnetic Fields

The right-hand rule is a mnemonic used to determine the direction of the magnetic field produced by a current in a wire. By pointing the thumb of your right hand in the direction of the current, your curled fingers indicate the direction of the magnetic field lines. This rule is essential when analyzing the combined effect of multiple currents on the direction of the overall magnetic field.

Ampère’s Law

Ampère’s Law provides a fundamental relationship between the magnetic field circulating a closed loop and the electric current passing through that loop. It is particularly useful in situations with symmetrical current distributions, such as with long straight wires, allowing for the derivation of the magnetic field formula and aiding in solving problems involving the magnetic interactions between conductors.

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