A small square loop of wire of side ell is pl | vedclass

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

Question

(C) The magnetic field $B$ at the center of a large square loop of side $L$ carrying current $i$ is given by:$B = 4 	imes \frac{\mu_0 i}{4 \pi (L/2)}

Vedclass · Accepted Answer

$128$

Vedclass · Answer

(C) The magnetic field $B$ at the center of a large square loop of side $L$ carrying current $i$ is given by:$B = 4 	imes \frac{\mu_0 i}{4 \pi (L/2)} (\sin 45^\circ + \sin 45^\circ) = \frac{\mu_0 i}{\pi L/2} 	imes \sqrt{2} = \frac{2\sqrt{2} \mu_0 i}{\pi L}$.Since $L \gg \ell$, we assume the magnetic field is uniform over the area of the small loop.The magnetic flux $\phi$ through the small loop of area $\ell^2$ is:$\phi = B 	imes \ell^2 = \frac{2\sqrt{2} \mu_0 i}{\pi L} \ell^2$.Given $L = \ell^2$, we substitute this into the expression:$\phi = \frac{2\sqrt{2} \mu_0 i}{\pi \ell^2} \ell^2 = \frac{2\sqrt{2} \mu_0 i}{\pi}$.The mutual inductance $M$ is defined as $M = \phi / i$:$M = \frac{2\sqrt{2} \mu_0}{\pi} = \frac{2\sqrt{2} (4\pi 	imes 10^{-7})}{\pi} = 8\sqrt{2} 	imes 10^{-7} 	ext{ H}$.$M = \sqrt{64 	imes 2} 	imes 10^{-7} 	ext{ H} = \sqrt{128} 	imes 10^{-7} 	ext{ H}$.Thus, $x = 128$.

$A$ small square loop of wire of side $\ell$ is placed inside a large square loop of wire of side $L$ $(L \gg \ell)$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x} \times 10^{-7} \text{ H}$, where $x = \dots$

Similar Questions

$A$ solenoid has $2000$ turns wound over a length of $0.30 \ m$. The area of its cross-section is $1.2 \times 10^{-3} \ m^2$. Around its central section,a coil of $300$ turns is wound. If an initial current of $2 \ A$ in the solenoid is reversed in $0.25 \ s$,the emf induced in the coil is equal to

Two concentric circular coils having radii $r_{1}$ and $r_{2}$ $(r_{2} \ll r_{1})$ are placed coaxially with centers coinciding. The mutual inductance of the arrangement is (Both coils have a single turn) ($\mu_{0} =$ permeability of free space).

In a pair of adjacent coils,if the current in one coil changes from $10 \,A$ to $2 \,A$ in a time $0.2 \,s$,an emf of $120 \,V$ is induced in the other coil. The mutual inductance of the pair of coils is: (in $\,H$)

$A$ long straight wire carrying current $I$ and a rectangular frame with side lengths $a$ and $b$ lie in the same plane as shown in the figure. The mutual inductance of the wire and frame is

With the decrease of current in the primary coil from $2\,A$ to zero in $0.01\,s$,the $emf$ generated in the secondary coil is $1000\,V$. The mutual inductance of the two coils is......$H$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module