Consider a conducting wire of length L bent i | vedclass

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

Question

(B) $1$. For the circular loop: The circumference is $2 \pi R = L$, so $R = \frac{L}{2 \pi}$.$2$. For the square loop: The perimeter is $4s = a$, wher

Vedclass · Accepted Answer

$\mu_{0} \frac{\pi a^{2}}{16 L}$

Vedclass · Answer

(B) $1$. For the circular loop: The circumference is $2 \pi R = L$, so $R = \frac{L}{2 \pi}$.$2$. For the square loop: The perimeter is $4s = a$, where $s$ is the side length of the square. Thus, $s = \frac{a}{4}$.$3$. The magnetic field $B$ at the centre of the circular loop due to a current $I$ flowing through it is $B = \frac{\mu_{0} I}{2R}$.$4$. Since $a \ll R$, the magnetic field $B$ is approximately uniform over the area of the square loop. The magnetic flux $\phi$ linked with the square loop is $\phi = B 	imes 	ext{Area of square} = B 	imes s^2$.$5$. Substituting the values: $\phi = \left( \frac{\mu_{0} I}{2R} ight) 	imes s^2 = \left( \frac{\mu_{0} I}{2(L / 2 \pi)} ight) 	imes \left( \frac{a}{4} ight)^2 = \left( \frac{\mu_{0} I \pi}{L} ight) 	imes \frac{a^2}{16} = \frac{\mu_{0} \pi a^2}{16 L} I$.$6$. The mutual inductance $M$ is given by $M = \frac{\phi}{I} = \frac{\mu_{0} \pi a^2}{16 L}$.

Similar Questions

$A$ small square loop of wire of side $l$ is placed inside a large square loop of wire of side $(L > l)$. The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to

Two coils $A$ and $B$ are placed in a circuit. When current in the coil $A$ changes by $0.8 \,A$, the magnetic flux in coil $B$ changes by $0.16 \,Wb$. The mutual inductance between the coils is (in $\,H$)

Two coils have mutual inductance $0.002 \ H$. The current changes in the first coil according to the relation $i = i_0 \sin \omega t$,where $i_0 = 5 \ A$ and $\omega = 50 \pi \ rad/s$. The maximum value of $emf$ in the second coil is $\frac{\pi}{\alpha} \ V$. The value of $\alpha$ is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module