Find the mutual inductance between two coaxia | vedclass

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

Question

(D) The magnetic field $B_1$ at the center of the second loop due to a current $i$ in the first loop is given by the formula for a magnetic dipole at

Vedclass · Accepted Answer

$\frac{{\mu _0 \pi a^4}}{{2l^3}}$

Vedclass · Answer

(D) The magnetic field $B_1$ at the center of the second loop due to a current $i$ in the first loop is given by the formula for a magnetic dipole at an axial distance $l$:$B_1 = \frac{{\mu _0}}{{4\pi }} \cdot \frac{{2M}}{{l^3}}$,where $M = i \cdot A = i(\pi a^2)$ is the magnetic moment of the first loop.Substituting $M$ into the expression for $B_1$:$B_1 = \frac{{\mu _0}}{{4\pi }} \cdot \frac{{2(i \pi a^2)}}{{l^3}} = \frac{{\mu _0 i a^2}}{{2l^3}}$.The magnetic flux $\phi_2$ through the second loop is $B_1 	imes A_2$,where $A_2 = \pi a^2$:$\phi_2 = \left( \frac{{\mu _0 i a^2}}{{2l^3}} ight) 	imes (\pi a^2) = \frac{{\mu _0 \pi a^4 i}}{{2l^3}}$.Since $\phi_2 = M_{12} i$,the mutual inductance $M_{12}$ is:$M_{12} = \frac{{\mu _0 \pi a^4}}{{2l^3}}$.

Find the mutual inductance between two coaxial circular loops of radius $a$ separated by a distance $l$,where $l >> a$.

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:

$A$ 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 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 $\pi$)

Two coils $A$ and $B$ are wound on the same iron core as shown in the figure. The number of turns in the coils $A$ and $B$ are $N_A$ and $N_B$ respectively. Identify the correct statement.

Two coils $A$ and $B$ have a coefficient of mutual inductance $M = 2 \ H$. The magnetic flux passing through coil $A$ changes by $4 \ Wb$ in $10 \ s$ due to the change in current in coil $B$. Then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module