The number of turns of two circular coils A a | vedclass

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

Question

(D) The magnetic moment $M$ of a circular coil is given by the formula $M = NIA$, where $N$ is the number of turns, $I$ is the current, and $A$ is the

Vedclass · Accepted Answer

$1: \sqrt{3}$

Vedclass · Answer

(D) The magnetic moment $M$ of a circular coil is given by the formula $M = NIA$, where $N$ is the number of turns, $I$ is the current, and $A$ is the area of the coil.Since the coil is circular, the area $A = \pi r^2$, where $r$ is the radius of the coil.Thus, $M = NI(\pi r^2)$.Given for coil $A$: $N_A = 300$, $M_A = M_1$, $r_A = r_1$.Given for coil $B$: $N_B = 200$, $M_B = M_2$, $r_B = r_2$.We are given $M_A / M_B = 1/2$ and $I_A = I_B = I$.Taking the ratio of the magnetic moments:$\frac{M_A}{M_B} = \frac{N_A I_A \pi r_A^2}{N_B I_B \pi r_B^2} = \frac{N_A}{N_B} \cdot \left(\frac{r_A}{r_B}\right)^2$.Substituting the known values:$\frac{1}{2} = \frac{300}{200} \cdot \left(\frac{r_A}{r_B}\right)^2$.$\frac{1}{2} = \frac{3}{2} \cdot \left(\frac{r_A}{r_B}\right)^2$.$\left(\frac{r_A}{r_B}\right)^2 = \frac{1}{2} \cdot \frac{2}{3} = \frac{1}{3}$.Therefore, $\frac{r_A}{r_B} = \frac{1}{\sqrt{3}}$.

The number of turns of two circular coils $A$ and $B$ are $300$ and $200$ respectively. The magnetic moments of the two coils $A$ and $B$ are in the ratio $1:2$. If the two coils carry equal currents, then the ratio of radii of coils $A$ and $B$ is

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 $N_A, I_A$ and $N_B, I_B$ are the number of turns and current of $A$ and $B$ respectively,then which of the following relations is correct?

$A$ thin circular disk of radius $R$ is uniformly charged with surface charge density $\sigma > 0$. The disk rotates about its central axis with a uniform angular speed $\omega$. The magnetic moment of the disk is:

The magnetic moment of a current $(i)$ carrying circular coil of radius $(r)$ and number of turns $(n)$ varies as

An insulating rod of length $l$ carries a charge $q$ distributed uniformly on it. The rod is pivoted at an end and is rotated at a frequency $f$ about a fixed perpendicular axis. The magnetic moment of the system is

$A$ circular coil of $1000$ turns and area of cross-section $1.5 \times 10^{-4} \, m^2$ is carrying a current of $2 \, A$. What is the magnetic moment associated with the coil in $Am^2$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module