A current i is flowing in a straight conductor of length L....

A current $\mathrm{i}$ is flowing in a straight conductor of length L. The magnetic induction at a point distant from its centre will be
(a) $\frac{4 \mu_0 i}{\sqrt{5} \pi L}$
(b) $\frac{\mu_0 i}{\sqrt{2} L}$
(c) $\frac{\mu_0 t}{2 \pi L}$
(d) zero

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Key Concepts

Angle Subtended at the Observation Point

For a finite conductor, the magnetic field at a point is determined by the angles that the ends of the wire make with the line perpendicular to the wire at the point. These angles are critical in the integration process, as the sine of these angles appears in the formula for the magnetic field derived from the Biot-Savart Law, explicitly indicating how the geometry of the conductor influences the resulting field.

Magnetic Field of a Finite Conductor

When dealing with a conductor of finite length, the calculation of the magnetic field requires integrating the contributions from each current element along the wire as given by the Biot-Savart Law. Unlike an infinitely long wire, the field produced by a finite conductor depends explicitly on the geometry and the angles subtended by the conductor at the observation point.

Biot-Savart Law

This fundamental principle relates the magnetic field produced at a point by a small segment of current-carrying conductor. It states that the contribution to the magnetic field from a current element is proportional to the current, the length of the element, and the sine of the angle between the element and the line connecting it to the observation point, and inversely proportional to the square of the distance from the element to the point.

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