Question

A long wire carr1es a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $\mathrm{B}$. It is then bent into a circular Loop of n turns. The magnetic field at the centre of the coil for same current will be. (a) $\mathrm{nB}$ (b) $\mathrm{n}^{2} \mathrm{~B}$ (c) $2 \mathrm{nB}$ (d) $2 \mathrm{n}^{2} \mathrm{~B}$

Name: Problem 1893, Chapter 13: JEE Physics
Uploaded: 2021-10-02T09:25:12-08:00
Duration: 1 min 23 s
Channel: Narayan Hari
Description: A long wire carr1es a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is B. It is then bent into a circular Loop of n turns. The magnetic field at the centre of the coil for same current will be. (a) nB (b) n^2 B (c) 2 nB (d) 2 n^2 B

   A long wire carr1es a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $\mathrm{B}$. It is then bent into a circular Loop of n turns. The magnetic field at the centre of the coil for same current will be.
(a) $\mathrm{nB}$
(b) $\mathrm{n}^{2} \mathrm{~B}$
(c) $2 \mathrm{nB}$
(d) $2 \mathrm{n}^{2} \mathrm{~B}$

JEE Physics

StemEZ 1st Edition

Chapter 13, Problem 1893

Instant Answer

Solved by Expert Narayan Hari

10/02/2021

Step 1

Step 1: The magnetic field at the center of a circular loop carrying a current is given by the formula: \[B = \frac{\mu_0 I}{2R}\] where $B$ is the magnetic field, $\mu_0$ is the permeability of free space, $I$ is the current, and $R$ is the radius of the Show more…

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A long wire carr1es a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $\mathrm{B}$. It is then bent into a circular Loop of n turns. The magnetic field at the centre of the coil for same current will be. (a) $\mathrm{nB}$ (b) $\mathrm{n}^{2} \mathrm{~B}$ (c) $2 \mathrm{nB}$ (d) $2 \mathrm{n}^{2} \mathrm{~B}$

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Key Concepts

Effect of Multiple Turns (Coils) on Magnetic Field

When a coil consists of multiple turns instead of just one, each individual loop contributes to the total magnetic field at the center. The contributions from each turn add linearly, meaning that if a single loop produces a field B, an n-turn coil will produce a magnetic field strength of nB provided the current remains constant and all turns have the same radius and lie in the same plane.

Magnetic Field of a Circular Current Loop

This concept deals with the magnetic field produced at the center of a circular loop carrying a steady current. The magnetic field from a single loop is determined using principles derived from the Biot-Savart Law, and its calculation provides a fundamental understanding of how currents generate magnetic fields in looped configurations.

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