Two parallel long straight conductors are placed at right...

Two parallel long straight conductors are placed at right angle to the meter scale at the $2 \mathrm{~cm}$ and $6 \mathrm{~cm}$ marks as shown in the figure. If they carry currents I and $3 \mathrm{I}$ respectively in the upward direction, then will produce zero magnetic field at

Key Concepts

Magnetic Field of a Long Straight Conductor

This concept describes how a steady current flowing through an infinitely long straight wire produces a magnetic field in the surrounding space. The magnitude of the field at a given distance is determined by Ampere's law, resulting in a field that decreases inversely with distance from the wire. This is foundational for understanding how currents produce magnetic fields.

Right-Hand Rule in Electromagnetism

The right-hand rule is a mnemonic used to determine the direction of the magnetic field generated by a current-carrying conductor. By pointing the thumb in the direction of the conventional current, the curl of the fingers indicates the circular direction of the magnetic field lines. This rule is crucial for analyzing the directional contributions of magnetic fields from different currents.

Superposition Principle for Magnetic Fields

The superposition principle states that the total magnetic field at any point in space is the vector sum of the magnetic fields produced by each current independently. This principle allows for the analysis of complex systems by considering the individual magnetic fields and then summing them, which is essential for determining points of zero net magnetic field.

Equating Magnetic Field Magnitudes for Cancellation

In problems where zero net magnetic field is sought, the individual magnetic fields produced by multiple sources are set equal in magnitude but opposite in direction. This requires establishing the relationship between the distances from each current-carrying conductor and their respective currents, highlighting the role of both magnitude and geometric configuration in producing field cancellation.

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