The magnetic field due to a current carrying circular loop...

The magnetic field due to a current carrying circular loop of radius $3 \mathrm{~cm}$ at a point on the axis at a distance of $4 \mathrm{~cm}$ from the centre is $54 \mu \mathrm{T}$. What will be its value at the centre of loop? (A) $125 \mu \mathrm{T}$ (B) $150 \mu \mathrm{T}$ (C) $250 \mu \mathrm{T}$ (D) $75 \mu \mathrm{T}$

The magnetic field due to a current carrying circular loop of radius $3 \mathrm{~cm}$ at a point on the axis at a distance of $4 \mathrm{~cm}$ from the centre is $54 \mu \mathrm{T}$. What will be its value at the centre of loop?
(A) $125 \mu \mathrm{T}$
(B) $150 \mu \mathrm{T}$
(C) $250 \mu \mathrm{T}$
(D) $75 \mu \mathrm{T}$

Key Concepts

Magnetic Field Due to a Current Loop

This concept involves determining the magnetic field produced by a steady current flowing in a loop. The calculation employs integral methods based on the Biot–Savart law to account for the contribution of each infinitesimal segment of the current-carrying conductor to the field at a point in space. It is fundamental in electromagnetism and is applicable in various devices such as electromagnets and inductors.

Biot–Savart Law

The Biot–Savart law is essential for calculating the magnetic field generated by a current element. It mathematically relates the magnetic field at a point to the current, the distance, and the orientation of the current element relative to that point. This law forms the basis for deriving expressions for the magnetic field of configurations such as current loops and solenoids.

On-Axis Magnetic Field Calculation

For a circular current loop, the magnetic field at a point along the axis perpendicular to the loop’s plane is derived by integrating the contributions of all current elements along the loop. This calculation results in a formula that depends on the loop’s radius, the distance of the point from the center along the axis, and the current, demonstrating how the field diminishes as one moves away from the loop.

Magnetic Field at the Centre of the Loop

The magnetic field at the very center of a current loop is a special case of the on-axis magnetic field where the distance from the center is zero. This simplifies the general expression significantly, yielding a result that is often used as a reference or a benchmark when comparing magnetic field strengths at different points around the loop.

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