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 $3 i$ respectively in the same direction, then they will produce zero magnetic field at (a) zero mark (b) $9 \mathrm{~cm}$ mark (c) $3 \mathrm{~cm}$ mark (d) $7 \mathrm{~cm}$ mark

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 $3 i$ respectively in the same direction, then they will produce zero magnetic field at
(a) zero mark
(b) $9 \mathrm{~cm}$ mark
(c) $3 \mathrm{~cm}$ mark
(d) $7 \mathrm{~cm}$ mark

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Key Concepts

Right-Hand Rule for Current-Carrying Conductors

The right-hand rule provides a method to determine the direction of the magnetic field created by a current-carrying conductor. According to this rule, if the thumb of the right hand points in the direction of the conventional current, the curled fingers indicate the direction of the magnetic field loops, which is essential for accurately analyzing the vector addition of fields.

Magnetic Field Due to a Long Straight Conductor

This principle states that the magnetic field generated by an infinitely long current-carrying conductor is given by the expression B = (??I)/(2?r), where I is the current and r is the distance from the wire. This concept is fundamental in understanding how magnetic fields diminish with increasing distance and how they depend directly on the magnitude of the current running through the conductor.

Superposition Principle for Magnetic Fields

The superposition principle asserts that when multiple magnetic fields are present at a given point, the net magnetic field is the vector sum of the individual fields. In contexts involving several current-carrying wires, this principle allows for the determination of points where fields may cancel each other, resulting in a net zero magnetic field.

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