A current of a 1 Amp is passed through a straight wire of...

A current of a $1 \mathrm{Amp}$ is passed through a straight wire of length 2 meter. The magnetic field at a point in air at a distance of 3 meters from either end of wire and lying on the axis of wire will be (a) $\left(\mu_{0} / 2 \pi\right)$ (b) $\left(\mu_{0} / 4 \pi\right)$ (c) $\left(\mu_{0} / 8 \pi\right)$ (d) zero

A current of a $1 \mathrm{Amp}$ is passed through a straight wire of length 2 meter. The magnetic field at a point in air at a distance of 3 meters from either end of wire and lying on the axis of wire will be
(a) $\left(\mu_{0} / 2 \pi\right)$
(b) $\left(\mu_{0} / 4 \pi\right)$
(c) $\left(\mu_{0} / 8 \pi\right)$
(d) zero

Key Concepts

Biot-Savart Law

The Biot-Savart Law is the fundamental principle used to calculate the magnetic field produced by a small element of current. It relates the magnetic field contribution from an infinitesimal segment of current carrying conductor to the magnitude and direction of the current, as well as the position of the point where the field is being measured. This concept is integral to determining the total field generated by a finite or infinite distribution of current-carrying elements.

Symmetry and Field Cancellation in Magnetostatics

When calculating the magnetic field at certain points relative to a finite current-carrying conductor, the symmetry of the arrangement can lead to complete cancellation of the magnetic field. For positions that lie along the axis of the current, contributions from different segments of the wire can cancel each other out, resulting in a net magnetic field of zero. This concept is essential in understanding how field vectors add up, particularly in configurations with high symmetry.

Magnetic Field Around a Current-Carrying Conductor

A current-carrying conductor produces a magnetic field that forms concentric circles around the wire, as described by the right-hand rule. This means that the field has a direction perpendicular to the length of the wire at any point, a fact which is crucial for understanding how the field lines are arranged in space relative to the conductor.

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