When a long wire carrying a steady current is bent into a...

When a long wire carrying a steady current is bent into a circular coil of one turn, the magnetic induction at its centre is $B$. When the same wire carrying the same current is bent to form a circular coil of $n$ turns of a smaller radius, the magnetic induction at the centre will be (A) $B / n$ (B) $n B$ (C) $B / n^{2}$ (D) $n^{2} B$

When a long wire carrying a steady current is bent into a circular coil of one turn, the magnetic induction at its centre is $B$. When the same wire carrying the same current is bent to form a circular coil of $n$ turns of a smaller radius, the magnetic induction at the centre will be
(A) $B / n$
(B) $n B$
(C) $B / n^{2}$
(D) $n^{2} B$

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Key Concepts

Magnetic Field of a Circular Current Loop

This concept details how a current flowing through a circular loop creates a magnetic field at its center, with the field strength determined by factors such as the current magnitude and the loop’s radius. The relationship is described by a formula that shows the magnetic induction is inversely proportional to the radius of the loop, emphasizing the role of geometry in magnetic field generation.

Dependence of Magnetic Field on Coil Geometry

This concept explains that the physical dimensions and configuration of a coil, such as the number of turns and the radius of each turn, directly affect the magnetic induction at its center. When a fixed length of wire is used, any change in the number of turns necessarily alters the radius of each loop, thereby impacting the resulting magnetic field according to the established geometric relations.

Effect of Multiple Turns on Magnetic Induction

In systems with multiple loops (or turns), the magnetic field at the center is the cumulative result of the field produced by each individual loop. When the loops are closely spaced and carry the same current, their individual contributions add linearly, illustrating how increasing the number of turns enhances the overall magnetic induction.

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