91影视

The electromagnetic effect on moving electric charges, electromagnetic fields, and magnetic materials is represented by a magnetic field, which is a vector field. In a magnetic flux, a moving charge generates a force that is perpendicular to both its own velocity and the magnetosphere.

From Faraday's law,

$蔚=\left|\frac{d{桅}_{\mathrm{m}}}{蔚}\right|.$

Where ${桅}_{\mathrm{m}}$is the flux through the loop which is the amount of magnetic field that flows through a loop of area localid="1648957060866" $A$and it is given by

${桅}_{\mathrm{m}}=BA$

Let us use this expression of localid="1648957068013" ${桅}_{\mathrm{m}}$into equation to get

$蔚=\frac{d\left(BA\right)}{dt}=B\frac{dA}{dt}.$

The radius of the loop $r$changes with time and we are given it in terms of time in the form

$r=r_o{e}^{-尾t}$

The area of the circular loop is calculated by

$A=蟺r^2=蟺{\left(r_o{e}^{-尾t}\right)}^2=蟺r_o^2{e}^{-2尾t}$

Now, we use the expression of $A$into equation and differentiate this equation to get the emf by

$$\begin{gathered} 蔚=B\frac{dA}{dt}=B\frac{d}{dt}\left(蟺r_o^2{e}^{-2尾t}\right) \\ 蔚==B蟺r_o^2(-2尾)e^{-2尾t} \\ 蔚=-2蟺r_o^2尾B{e}^{-2尾t}. \end{gathered}$$