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# Modified Ampere's law explanation

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Show why the math for amperes time dependent equation is right.

At a site they derive the amperes law for a changing electrical field. I know that B is related to current. But what I wanted was an illustration for how the mathematical justification in the attachment is right by pointing out where the dE/dt effects the magnetic field.

See the attachment.

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https://brainmass.com/physics/amperes-law/modified-amperes-law-explanation-592206

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A condensed version is provided below - see attached file for equations.

The current density vector J is defined as the change in charge per unit area per unit time.
So, if we integrate the current density over a surface S, we get the change in charge per unit time on that surface - the current flowing through the surface.
We write it as:
(1.1)
Now assume we have a surface that ...

#### Solution Summary

The solution explains how to obtain the modified Amperes law with time dependent electric fields.

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