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  • An expression for the magnetic field strength B at the point between the capacitor plates indicates in figure express B in terms of the rate of change of the electric field strength ie, <img alt="\

An expression for the magnetic field strength B at the point between the capacitor plates indicates in figure express B in terms of the rate of change of the electric field strength ie, \frac{d E}{d t} between the plates

Option: 1

\frac{\mu_o}{2 \pi r}  


Option: 2

zero


Option: 3

\frac{\mu_o}{2 r}


Option: 4

\frac{\epsilon_o \mu_o r}{2} \frac{d E}{d t}


Answers (1)

By modified ampere's law -

\oint \vec {B}.\vec{dl}=\mu_{o}i+\mu_{o}\epsilon _{o}\frac{d\phi_{E}}{dt}

The line integral of the magnetic field is equal to \mu_{o} times the total current (conduction + displacement)

Here conduction current is zero, 

\therefore \oint \vec {B}.\vec{dl}=\mu_{o}\epsilon _{o}\frac{d\phi_{E}}{dt}

\\ \oint {B} {dl} \cos 0^o=\mu_{o}\epsilon _{o}\frac{d\phi_{E}}{dt} \\ \text{B is constant for loop of radius r} \\ {B} \oint {dl} =\mu_{o}\epsilon _{o}\frac{d({EA cos 0^o})}{dt} \\ {B} (2 \pi r) =\mu_{o}\epsilon _{o} (\pi r^2)\frac{d {E}}{dt}
\begin{aligned} &B=\frac{\mu_{o}}{2 \pi r} \times \epsilon _o \frac{d \phi_{E}}{d t} \\ &=\frac{\mu_{o} \varepsilon_{o} \pi r^{2} }{2 \pi r } \times \frac{dE}{dt} \\ &B=\frac{\mu_{o} \varepsilon_{o} r }{2 } \times \frac{dE}{dt} \end{aligned}

 

Posted by

Sumit Saini

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