a) Substituting the above equations in the following equation we get
${c}
\oint E . d l=-\frac{d \phi_{B}}{d t}=-\frac{d}{d t} \oint B \cdot d s$
So,
$E_{0} / B_{0}=0$
b)
We get $c=1 / \sqrt{\mu}_{0} \varepsilon_{0}$
A plane EM wave travelling in vacuum along z-direction is given by $E=E_{0} \sin (k z-\omega t) \hat{i} \text { and } B=B_{0} \sin (k z-\omega t) \hat{j}$
a) Use equation $\oint E . d l=\frac{-d \phi_{B}}{d t}$ to prove $E_ 0 / \mathbf B_ 0=\mathrm{c}$
b) by using a similar process and the equation $\oint B . d l=\mu_{0} I \epsilon_{0} \frac{-d \phi_{E}}{d t}$, prove that $c=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}$
a) Use equation $\oint E . d l=\frac{-d \phi_{B}}{d t}$ to prove $E_ 0 / \mathbf B_ 0=\mathrm{c}$
b) by using a similar process and the equation $\oint B . d l=\mu_{0} I \epsilon_{0} \frac{-d \phi_{E}}{d t}$, prove that $c=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}$
A plane EM wave travelling in vacuum along z-direction is given by $E=E_{0} \sin (k z-\omega t) \hat{i} \text { and } B=B_{0} \sin (k z-\omega t) \hat{j}$
a) Use equation $\oint E . d l=\frac{-d \phi_{B}}{d t}$ to prove $E_ 0 / \mathbf B_ 0=\mathrm{c}$
b) by using a similar process and the equation $\oint B . d l=\mu_{0} I \epsilon_{0} \frac{-d \phi_{E}}{d t}$, prove that $c=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}$
a) Use equation $\oint E . d l=\frac{-d \phi_{B}}{d t}$ to prove $E_ 0 / \mathbf B_ 0=\mathrm{c}$
b) by using a similar process and the equation $\oint B . d l=\mu_{0} I \epsilon_{0} \frac{-d \phi_{E}}{d t}$, prove that $c=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}$