Two parallel long wires A and B carry currents i1 and i2(<i1) . When i1 and i2 are in the same d

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Two parallel long wires A and B carry currents i1 and...

Two parallel long wires $A$ and $B$ carry currents $i_{1}$ and $i_{2}\left(<i_{1}\right) .$ When $i_{1}$ and $i_{2}$ are in the same direction, the magnetic field at a point mid way between the wires is $10 \mu \mathrm{T}$. If $i_{2}$ is reversed, the field becomes $30 \mu \mathrm{T}$. The ratio, $i_{1} / i_{2}$ is (a) 1 (b) 2 (c) 3 (d) 4

Key Concepts

Effect of Current Direction on Magnetic Field Orientation

The direction of the magnetic field produced by a current-carrying conductor follows the right-hand rule. When currents flow in the same direction, their magnetic fields at a point between the wires may oppose or reinforce one another depending on their orientation. Conversely, when the current in one wire is reversed, the relative orientations of the magnetic fields change, leading to different net field magnitudes. This concept is key to understanding changes in measured magnetic fields based on current directions.

Superposition Principle in Electromagnetism

The superposition principle states that the net magnetic field created by multiple sources is the vector sum of the individual magnetic fields produced by each source. This principle is essential for problems involving multiple current-carrying wires, as the overall magnetic field at any point is determined by adding the contributions from each wire, considering both their magnitudes and directions.

Magnetic Field of a Long Current-Carrying Wire

This concept refers to the magnetic field produced by a straight, electrically conducting wire carrying current. According to Ampère's law, the field's magnitude at a given distance from the wire is proportional to the current and inversely proportional to the distance. Understanding this concept is crucial because it forms the basis for analyzing the magnetic effects of currents in long, parallel wires.

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