A length of wire carries a steady current. It is bent first...

Name: Problem 22, Chapter 15: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-10-06T10:25:54-08:00
Duration: 1 min 46 s
Channel: Aja S
Description: A length of wire carries a steady current. It is bent first to form a circular coil of one turn. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre caused by the same current is (A) a quarter of its first value. (B) unaltered. (C) four times of its first value. (D) half of its first value.

A length of wire carries a steady current. It is bent first to form a circular coil of one turn. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre caused by the same current is (A) a quarter of its first value. (B) unaltered. (C) four times of its first value. (D) half of its first value.

A length of wire carries a steady current. It is bent first to form a circular coil of one turn. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre caused by the same current is
(A) a quarter of its first value.
(B) unaltered.
(C) four times of its first value.
(D) half of its first value.

Key Concepts

Magnetic Field from a Current Loop

This concept involves determining the magnetic field at the center of a circular loop carrying a steady current. The field is given by the relation B = (??I)/(2R), highlighting how it depends on the current I and the loop's radius R. This fundamental formula is crucial for analyzing magnetic fields produced by current-carrying loops in electromagnetism.

Dependence of Magnetic Field on Loop Radius

This concept focuses on how the magnitude of the magnetic field changes with the radius of the loop. Since the magnetic field is inversely proportional to the radius, a smaller loop yields a higher field strength at its center. Recognizing this inverse relationship is key when comparing configurations made from a wire of fixed length.

Effect of Coil Turns

This concept deals with the enhancement of the magnetic field by having multiple turns in a coil. When the wire is reformed into a coil with more than one turn, the fields contributed by individual loops add up, increasing the total magnetic field at the center proportionally to the number of turns.

Geometric Constraints in Wire Shaping

This concept addresses how the fixed length of the wire limits the possible dimensions of the constructed shapes. For example, forming a single loop requires a longer circumference compared to forming multiple smaller loops, which affects the loop’s radius and consequently the magnetic field generated. Understanding these constraints is essential in comparing different geometric configurations derived from the same wire length.

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