91影视

This law is used to determine the electromotive force (emf) generated due to the interaction between a magnetic field and an electric conductor.

Based on this law, the amount of emf induced in a conductor directly relies upon the changes in the magnetic flux

The magnetic monopole is,$q_m.$

The self-inductance of the resistanceless loop of wire is, L .

The generalised equation of Faraday鈥檚 law for the resistanceless loop of wire is given by,

$鈭�脳E=-{渭}_0{J}_m-\frac{鈭�B}{鈭�t}$

Here,represents the electric field,${渭}_0$is the permeability of free space,$J_m$is the current of magnetic charge and$\frac{鈭�B}{鈭�t}$is the change in magnetic field.

Integrating both sides of equation over the da surface,

$$\begin{gathered} 鈭�(鈭�脳E).da=鈭�\left(-{渭}_0{J}_m-\frac{鈭�B}{鈭�t}\right).da \\ 鈭�E.dl=鈭�-{渭}_0{J}_m.da-鈭�\frac{鈭�B}{鈭�t}.da \\ 蔚=-{渭}_0{J}_m.da-\frac{d}{dt}鈭�B.da \\ 蔚=-{渭}_0{l}_{menc}-\frac{d桅}{dt} \end{gathered}$$

Here,the induced emf,$l_{m_{enc}}$is induced electro-magnetic current and$\frac{d桅}{dt}$is the change in the magnetic flux.

Also, the induced emf in the wire loop is given by,

$蔚=-L\frac{dl}{dt}$

Equating both values,

$$\begin{gathered} -L\frac{dl}{dt}=-{渭}_0{l}_{m_{enc}}-\frac{d桅}{dt} \\ \frac{dl}{dt}=\frac{-{渭}_0}{L}{l}_{m_{enc}}+\frac{1}{L}\frac{d桅}{dt} \\ l=\frac{{渭}_0}{L}鈭�Q_m+\frac{1}{L}鈭�桅 \end{gathered}$$

Here,$鈭�Q_m$is the total magnetic charge passing through the surface,$鈭�桅$is the change in flux through the surface.

For theresistanceless loop of wire, and .

$$\begin{gathered} l=\frac{{渭}_0}{L}脳q_m+\frac{1}{L}脳0 \\ l=\frac{{渭}_0{q}_m}{L} \end{gathered}$$

Hence, the induced current in the loop is$l=\frac{{渭}_0{q}_m}{L}.$