Understanding Maxwell's Equations: Integral and Differential Forms

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Maxwell's equations can be expressed in both integral and differential forms, which can lead to confusion due to the use of different symbols like B for magnetic field and H for magnetic field intensity. The equations also vary based on whether they include charge density (\rho) or current density (J). Understanding the context in which each form is used is crucial for applying them correctly in problems. The integral forms are typically used for macroscopic scenarios, while differential forms are more suited for local field analysis. Clarifying these distinctions can help in tackling related homework questions effectively.
girlinphysics
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I am getting really confused with the millions of different versions/forms of Maxwell's equations. I know there is differential form and integral form, but sometimes there is a B for magnetic field...other times there is an H. Sometimes there is dependence on \rho or J (current density) and sometimes there isn't.

If someone could clarify those confusions and provide a concrete set of both integral and differential forms hopefully I can tackle a few homework questions I have been given on them.
 
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The Wikipedia article seems to cover this really well. Link.
 

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