Question

A wire of length $L \mathrm{~m}$ carrying a current $I$ amp is bent in the form of a circle. The magnitude of magnetic moment is : (a) $\frac{I L^{2}}{4 \pi}$ (b) $\frac{I L^{2}}{2 \pi}$ (c) $\frac{1 L}{4 \pi}$ (d) $I \pi L^{2}$

Name: Problem 16, Chapter 27: Arihant AIEEE Physics
Uploaded: 2021-10-06T16:20:51-08:00
Duration: 2 min 13 s
Channel: Vysakh M
Description: A wire of length L m carrying a current I amp is bent in the form of a circle. The magnitude of magnetic moment is : (a) (I L^2)/(4 π) (b) (I L^2)/(2 π) (c) (1 L)/(4 π) (d) I πL^2

   A wire of length $L \mathrm{~m}$ carrying a current $I$ amp is bent in the form of a circle. The magnitude of magnetic moment is :
(a) $\frac{I L^{2}}{4 \pi}$
(b) $\frac{I L^{2}}{2 \pi}$
(c) $\frac{1 L}{4 \pi}$
(d) $I \pi L^{2}$

Arihant AIEEE Physics

D.B. Singh 2006 Edition

Chapter 27, Problem 16

Instant Answer

Solved by Expert Vysakh M

10/06/2021

Step 1

We need to find the magnetic moment of this setup. The formula for magnetic moment ($\mu$) is given by $\mu = I \cdot A$, where $I$ is the current and $A$ is the area. Show more…

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A wire of length $L \mathrm{~m}$ carrying a current $I$ amp is bent in the form of a circle. The magnitude of magnetic moment is : (a) $\frac{I L^{2}}{4 \pi}$ (b) $\frac{I L^{2}}{2 \pi}$ (c) $\frac{1 L}{4 \pi}$ (d) $I \pi L^{2}$

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Key Concepts

Geometric Relationships in Circles

When a wire is bent into a circle, its length becomes the circumference of the circle. Using the relationship between circumference and radius, one can derive the area of the circle. This geometric understanding is essential in relating the physical dimensions of the wire to the properties of the resulting magnetic moment.

Magnetic Moment of a Current Loop

This concept states that the magnetic moment of a loop carrying an electric current is given by the product of the current and the area enclosed by the loop. It is a measure of the strength and orientation of the magnetic dipole created by the current and is fundamental in understanding magnetic interactions of current-carrying conductors.

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