A current carrying wire of length L is transf | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The magnetic moment $M$ of a coil is given by $M = N I A$,where $N$ is the number of turns,$I$ is the current,and $A$ is the area of the coil.For

Vedclass · Accepted Answer

Must have just one turn and would be circular in shape

Vedclass · Answer

(A) The magnetic moment $M$ of a coil is given by $M = N I A$,where $N$ is the number of turns,$I$ is the current,and $A$ is the area of the coil.For a circular coil of $N$ turns and radius $R$,the total length of the wire is $L = N(2 \pi R)$,which implies $R = \frac{L}{2 \pi N}$.The area of the circular coil is $A = \pi R^2 = \pi \left( \frac{L}{2 \pi N} \right)^2 = \frac{L^2}{4 \pi N^2}$.Substituting this into the magnetic moment formula: $M = N I \left( \frac{L^2}{4 \pi N^2} \right) = \frac{I L^2}{4 \pi N}$.Since $I$,$L$,and $\pi$ are constants,$M$ is inversely proportional to $N$ $(M \propto \frac{1}{N})$.To maximize $M$,we must minimize $N$. Therefore,$N = 1$ gives the maximum magnetic moment.For a fixed perimeter,a circle encloses the maximum area compared to other shapes,so the coil must be circular.

$A$ current carrying wire of length $L$ is transformed into a coil of $N$ turns. To achieve maximum magnetic moment,the coil

Similar Questions

The magnetic moments associated with two closely wound circular coils $A$ and $B$ of radius $r_A = 10 \ cm$ and $r_B = 20 \ cm$ respectively are equal if: (Where $N_A, I_A$ and $N_B, I_B$ are the number of turns and current of $A$ and $B$ respectively)

$A$ current $I$ is flowing in a conductor of length $L$. When it is bent in the form of a circular loop,its magnetic moment will be

$A$ charged particle going around in a circle can be considered to be a current loop. $A$ particle of mass $m$ carrying charge $q$ is moving in a plane with speed $v$ under the influence of magnetic field $\overrightarrow{ B }$. The magnetic moment of this moving particle is:

$A$ thin disc of radius $R$ and mass $M$ has charge $q$ uniformly distributed on it. It rotates with angular velocity $\omega$. The ratio of magnetic moment and angular momentum for the disc is

$A$ closely wound solenoid of $800$ turns and area of cross-section $2.5 \times 10^{-4} \; m^2$ carries a current of $3.0 \; A$. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?

Vedclass Test Series

Exam Paper Generator

Online Exam Module