# How is the equation for Ampere’s circuital law modified in the presence of displacement current? Explain.

The current which comes into existence, with addition to conduction current, whenever electric flux or electric field changes with time, is known as displacement current.

Hence, to maintain the dimensional consistency, the displacement current is given as ;

$I_{d}=\varepsilon _{o}\frac{d\phi \varepsilon }{dt}$

Where, $\phi _{E}$ = electric flux

therefore, the total current across the closed loop will be ;

$= I_{c}+I_{d}$

$= I_{c}+\varepsilon _{o}\frac{d\phi }{dt}$             $(\because I_{d}=\varepsilon _{o}\frac{d\phi \varepsilon }{dt})$

Hence, the Ampere's circuital law with Maxwell modification is

$\oint B.dl=\mu _{o}\left [ I_{c}+\varepsilon _{o}\frac{d\phi \varepsilon }{dt} \right ]$

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