A circular current loop of radius R is placed | vedclass

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

Question

(D) The magnetic field $B$ produced by the square loop at its center is $B = \frac{\mu_0 I}{\pi} \frac{4 \sin(45^\circ)}{L} = \frac{2\sqrt{2}\mu_0 I}{

Vedclass · Accepted Answer

$2\sqrt{2} \frac{\mu_0 R^2}{L}$

Vedclass · Answer

(D) The magnetic field $B$ produced by the square loop at its center is $B = \frac{\mu_0 I}{\pi} \frac{4 \sin(45^\circ)}{L} = \frac{2\sqrt{2}\mu_0 I}{\pi L}$.Since the circular loop is very small $(L >> R)$, we assume the magnetic field $B$ is uniform over the area of the circular loop.The magnetic flux $\phi$ linked with the circular loop of radius $R$ is $\phi = B 	imes A = B 	imes (\pi R^2)$.Substituting the value of $B$, we get $\phi = \left( \frac{2\sqrt{2}\mu_0 I}{\pi L} ight) 	imes (\pi R^2) = \frac{2\sqrt{2}\mu_0 I R^2}{L}$.The mutual inductance $M$ is defined as $M = \phi / I$.Therefore, $M = \frac{2\sqrt{2}\mu_0 R^2}{L}$.

$A$ circular current loop of radius $R$ is placed inside a square loop of side length $L$ $(L >> R)$ such that they are co-planar and their centers coincide. The permeability of free space is $\mu_0$. The mutual inductance between the circular loop and the square loop is . . . . . . .

Similar Questions

Two coils $A$ and $B$ having turns $300$ and $600$ respectively are placed near each other. On passing a current of $3.0 \ A$ in coil $A$, the magnetic flux linked with coil $A$ is $1.2 \times 10^{-4} \ Wb$ and with coil $B$ it is $9.0 \times 10^{-5} \ Wb$. The mutual inductance of the system is:

Two coils have a mutual inductance of $0.004 \ H$. The current changes in the first coil according to the equation $I = I_0 \sin \omega t$,where $I_0 = 10 \ A$ and $\omega = 50 \pi \ rad \ s^{-1}$. The maximum value of e.m.f. in the second coil in volt is (in $\pi$)

The dimension of mutual inductance is ............

$A$ pair of adjacent coils has a mutual inductance of $1.5\; H$. If the current in one coil changes from $0$ to $20\; A$ in $0.5\; s$,what is the change of flux (in $Wb$) linkage with the other coil?

Vedclass Test Series

Exam Paper Generator

Online Exam Module