Why is the following situation impossible? Two parallel...

Why is the following situation impossible? Two parallel copper conductors each have length $\ell=0.500 \mathrm{m}$ and radius $r=250 \mu \mathrm{m} .$ They carry currents $I=10.0 \mathrm{A}$ in opposite directions and repel each other with a magnetic force $F_{B}=$ $1.00 \mathrm{N} .$

Key Concepts

Magnetic Force Between Parallel Currents

This concept explains that two parallel current?carrying conductors exert forces on one another due to the magnetic fields they produce. Ampère’s force law quantitatively describes the mutual attraction or repulsion between currents, depending on their directions, with the force per unit length being proportional to the product of the currents divided by the distance between them. In this problem, the calculation based on the given currents, conductor lengths, and wire dimensions leads to an unrealistic force value, illustrating the infeasibility of the scenario.

Magnetic Field Produced by a Current-Carrying Conductor

According to the Biot–Savart law, a steady current flowing through a wire produces a magnetic field that circulates around the wire. The strength of this field decreases inversely with distance from the wire. In evaluating the scenario, one must consider whether the magnetic field generated by such currents in conductors of a given size can create the proposed magnetic force, which turns out to be inconsistent with established electromagnetic theory.

Lorentz Force on a Current-Carrying Conductor

The Lorentz force law stipulates that a current-carrying conductor placed in a magnetic field experiences a force perpendicular to both the direction of the current and the magnetic field. This force is what causes the interaction (attraction or repulsion) between two wires carrying current. In the context of the problem, using this law to compute the force on each conductor reveals that the purported magnitude of repulsive force is not physically attainable given the dimensions and current values provided.

Consistency of Physical Parameters

This concept emphasizes the importance of verifying whether the numerical values for physical parameters such as wire radius, length, current, and the resulting force are consistent with known electromagnetic principles. In the given scenario, a calculation based on standard equations shows that the expected force between the wires cannot realistically reach the stated 1.00 N, indicating that the situation presented is impossible due to contradictory or nonphysical parameter choices.

Transcript

Please give Ace some feedback