A wire carrying current I and other carrying 2 I in the same...

A wire carrying current $I$ and other carrying $2 I$ in the same direction produces a magnetic field $B$ at the mid point. What will be the field when $2 I$ wire is switched off?
(A) $B / 2$
(B) $2 B$
(C) $B$
(D) $4 \underline{B}$

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Key Concepts

Magnetic Field of a Straight Conductor

This concept involves the formula for the magnetic field produced by a long, straight current?carrying conductor. According to Ampère’s law (or the Biot–Savart law), the magnetic field at a distance r from a straight wire carrying current I is given by B = (??I)/(2?r). This relationship is central in calculating the contribution of each wire's current to the magnetic field at a given point.

Superposition Principle

The superposition principle states that the total magnetic field created by several current-carrying wires is the vector sum of the individual fields produced by each wire independently. In problems involving multiple wires, this principle is used to determine the net magnetic field at a point by adding or subtracting the fields from each wire, taking into account their magnitudes and directions.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic field produced by a current-carrying conductor. By pointing the thumb of the right hand in the direction of the conventional current, the curl of the fingers indicates the circular direction of the magnetic field around the conductor. This rule is crucial when assessing whether fields from multiple currents add or oppose each other at a specific location.

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