Question

$\huge\red{\boxed{\sf QuEStiON}}$


A capacitor, made of two parallel plates each of plate area A and separation d, is being charged by an external ac source. Show that the displacement current inside the capacitor is the same as the current charging the capacitor.​

Answer 1

Explanation:

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Answer 2

Answer:

$\sf\bold\red{AnswEr}$

$</p><p>TD = ε0dμEdt \\ \\ let \: the \: altering \: emf \: charging \: the \: plates \: of \: capacitor mbem E=E0 \: sinωt. \\ \\ charge \: on \: the \: capacitor \:  q=EC=CE0 \: sinωt \\ \\ I = \frac{dq}{dt} = \frac{d}{dt} </p><p>(CE0sinωt)=ωCE0cosωt=I0cosωt \: \: (where \: I0=ωCE0) \\ \\ Displacement \: current \\ \\ ID=ε0 \frac{dψ</p><p>E</p><p>}{dt} =ε0A \frac{dE}{dt} =ε0A \frac{d( \frac{q}{ε0A}) }{dt} ( \frac{CE0sinωt}{ε0A} )</p><p></p><p></p><p></p><p></p><p> \\ \\ = \frac{ d}{dt} (CE0sinωt) = ωCE0cosωt=I0cosωt \\ \\ Thus \: the \: displacement \: current \: inside \: the \: capacitor \: is \: the \: same \: as \: current \: charging \: the \: capacitor.</p><p></p><p>$