A circular wire loop of radius R is placed in | vedclass

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

Question

(B) The magnetic field $B$ on the axis of a circular loop of radius $R$ at a distance $X$ from the center is given by:$B = \frac{\mu_0 i R^2}{2(R^2 +

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(B) The magnetic field $B$ on the axis of a circular loop of radius $R$ at a distance $X$ from the center is given by:$B = \frac{\mu_0 i R^2}{2(R^2 + X^2)^{3/2}}$Given $X = \sqrt{3} R$,the magnetic field at the center of the square loop is:$B = \frac{\mu_0 i R^2}{2(R^2 + 3R^2)^{3/2}} = \frac{\mu_0 i R^2}{2(4R^2)^{3/2}} = \frac{\mu_0 i R^2}{2 \cdot 8 R^3} = \frac{\mu_0 i}{16 R}$Since the square loop has $N = 2$ turns,area $A = a^2$,and the angle between the area vector and the magnetic field (which is along the $z$-axis) is $	heta = 45^{\circ}$,the magnetic flux $\phi$ is:$\phi = N B A \cos(45^{\circ}) = 2 \cdot \left(\frac{\mu_0 i}{16 R}ight) \cdot a^2 \cdot \frac{1}{\sqrt{2}} = \frac{\mu_0 i a^2}{8 \sqrt{2} R}$Since $\sqrt{2} = 2^{1/2}$ and $8 = 2^3$,the denominator is $2^3 \cdot 2^{1/2} = 2^{7/2}$.Thus,$\phi = \frac{\mu_0 i a^2}{2^{7/2} R}$.The mutual inductance $M$ is defined as $M = \frac{\phi}{i} = \frac{\mu_0 a^2}{2^{7/2} R}$.Comparing this with the given expression $\frac{\mu_0 a^2}{2^{p/2} R}$,we get $p = 7$.

Similar Questions

Two coils have a mutual inductance of $ 0.005 \ H $. The current changes in the first coil according to the equation $ i = i_{m} \sin \omega t $,where $ i_{m} = 10 \ A $ and $ \omega = 100 \pi \ rad \ s^{-1} $. The maximum value of the emf induced in the second coil is:

Two planar concentric rings of metal wire having radii $r_1$ and $r_2$ (with $r_1 > r_2$) are placed in air. The current $I$ is flowing through the coil of larger radius. The mutual inductance between the coils is given by ($\mu_0$ = permeability of free space)

The mutual inductance of a pair of coils,each of $N$ turns,is $M$ henry. If a current of $I$ ampere in one of the coils is brought to zero in $t$ seconds,the e.m.f. induced per turn in the other coil in volt is:

The emf induced in the secondary coil due to unit rate of change of current in the primary is called

Vedclass Test Series

Exam Paper Generator

Online Exam Module