# Modified Ampere's law explanation

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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#### Solution Preview

The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

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.