Displacement current

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Question

Inside a parallel plate capacitor the electric field E varies with time as $t^{2}$ . The variation of induced magnetic field with time is given by :

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Solution

For a given plate circumference = L (constant ) and area of plate = A (constant)
$\begin{array}{l} \int B d l = μ_{0} i_{D} = μ_{0} ε_{0} \frac{d ϕ_{E}}{d t} \\ B L = μ_{0} ε_{0} A \frac{d E}{d t} \\ B \propto \frac{d E}{d t} \\ \frac{d B}{d t} \propto \frac{d^{2} E}{d t^{2}} ........(1) \\ E = k t^{2} \\ \frac{d E}{d t} = 2 k t \\ \frac{d^{2} E}{d t^{2}} = 2 k = c o n s \tan t \\ \Rightarrow \frac{d B}{d t} = c o n s \tan t \end{array}$

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Displacement current

Remember concepts with our Masterclasses.

Inside a parallel plate capacitor the electric field E varies with time as t2. The variation of induced magnetic field with time is given by :

For a given plate circumference = L (constant ) and area of plate = A (constant)∫Bdl = μ0iD=μ0ε0 dϕEdtBL=μ0ε0 A dEdtB ∝ dEdtdBdt ∝ d2Edt2........(1)E=kt2dEdt = 2ktd2Edt2=2k=constant⇒ dBdt = constant

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Inside a parallel plate capacitor the electric field E varies with time as $t^{2}$ . The variation of induced magnetic field with time is given by :