A small square loop of wire of side l is plac | vedclass

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

Question

(D) Let a current $I$ flow through the large square loop of side $L$. The magnetic field $B$ produced by one side of the large loop at its centre is g

Vedclass · Accepted Answer

$\frac{l^2}{L}$

Vedclass · Answer

(D) Let a current $I$ flow through the large square loop of side $L$. The magnetic field $B$ produced by one side of the large loop at its centre is given by the formula for a finite wire: $B_{side} = \frac{\mu_0 I}{4 \pi d} (\sin \alpha + \sin \beta)$,where $d = L/2$ and $\alpha = \beta = 45^\circ$.Since there are four such sides,the total magnetic field at the centre is $B = 4 	imes \frac{\mu_0 I}{4 \pi (L/2)} (\sin 45^\circ + \sin 45^\circ) = \frac{\mu_0 I}{\pi L} 	imes 2 	imes \frac{2}{\sqrt{2}} = \frac{2 \sqrt{2} \mu_0 I}{\pi L}$.Since $L \gg l$,we can assume the magnetic field $B$ is uniform over the area of the smaller loop $S_2 = l^2$.The magnetic flux linked with the smaller loop is $\phi_2 = B 	imes S_2 = \left( \frac{2 \sqrt{2} \mu_0 I}{\pi L} ight) l^2$.The mutual inductance $M$ is defined as $M = \frac{\phi_2}{I} = \frac{2 \sqrt{2} \mu_0 l^2}{\pi L}$.Therefore,$M \propto \frac{l^2}{L}$.

$A$ small square loop of wire of side $l$ is placed inside a large square loop of side $L$ $(L \gg l)$. If the loops are coplanar and their centres coincide,the mutual inductance of the system is directly proportional to :

Similar Questions

Two coils have a mutual inductance $0.005 \, H$. The current changes in the first coil according to the equation $I = I_0 \sin(\omega t)$,where $I_0 = 10 \, A$ and $\omega = 100\pi \, rad/s$. The maximum value of the $e.m.f.$ in the second coil is:

Derive the formula for mutual inductance of two very long coaxial solenoids. Also,discuss the reciprocity theorem.

$A$ 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

Two coils have a mutual inductance of $0.01 \ H$. The current in the first coil changes according to the equation $I = 5 \sin(200 \pi t)$. The maximum value of the e.m.f. induced in the second coil is:

If a change in current of $0.01 \,A$ in one coil produces a change in magnetic flux of $2 \times 10^{-2} \,Wb$ in the other coil,then the mutual inductance of the two coils in henry is (in $\,H$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module