A circular current carrying coil has a radius R. The...

A circular current carrying coil has a radius $R$. The distance from the centre of the coil on the axis where the magnetic induction will be $\frac{1}{8}$ th of its value at the centre of the coil, is: (a) $R \sqrt{3}$ (b) $\frac{R}{\sqrt{3}}$ (c) $\frac{2 R}{\sqrt{3}}$ (d) $(2 \sqrt{3}) R$

A circular current carrying coil has a radius $R$. The distance from the centre of the coil on the axis where the magnetic induction will be $\frac{1}{8}$ th of its value at the centre of the coil, is:
(a) $R \sqrt{3}$
(b) $\frac{R}{\sqrt{3}}$
(c) $\frac{2 R}{\sqrt{3}}$
(d) $(2 \sqrt{3}) R$

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Key Concepts

Magnetic Field Along the Axis of a Circular Loop

For a circular current loop, the magnetic field along its axis can be expressed by a formula that includes the loop’s radius and the distance from its center. This relationship shows that the magnetic field decreases with increasing distance from the center following a specific power law, highlighting the spatial decay of the field in a symmetric system.

Algebraic Analysis in Electromagnetic Problems

In electromagnetic theory, solving for parameters like distances where the magnetic field reaches a specified fraction of a reference value involves setting up equations based on the field expressions and manipulating them algebraically. This process often includes handling exponents and roots to isolate and compute the desired variable.

Biot-Savart Law

The Biot-Savart Law provides the fundamental relation to calculate the magnetic field generated by a current-carrying element. It is applied to derive the magnetic field at any point due to distributions of current, such as those in a circular loop, and serves as the basis for understanding how current elements contribute to the overall magnetic field.

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