The Maxwell-modified form of Ampere's circuit | vedclass

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(C) Ampere's original circuital law was found to be inconsistent for time-varying electric fields.James Clerk Maxwell introduced the concept of displa

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$\oint \vec{B} \cdot d\vec{l} = \mu_0 i + \mu_0 \epsilon_0 \frac{d\phi_E}{dt}$

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(C) Ampere's original circuital law was found to be inconsistent for time-varying electric fields.James Clerk Maxwell introduced the concept of displacement current,$I_d = \epsilon_0 \frac{d\phi_E}{dt}$,to resolve this inconsistency.The modified Ampere-Maxwell law states that the line integral of the magnetic field around any closed path is equal to $\mu_0$ times the sum of the conduction current $i$ and the displacement current $I_d$.Mathematically,this is expressed as: $\oint \vec{B} \cdot d\vec{l} = \mu_0 (i + I_d) = \mu_0 i + \mu_0 \epsilon_0 \frac{d\phi_E}{dt}$.

The Maxwell-modified form of Ampere's circuital law is .......

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