I Which Form of Maxwell's Equations is More Useful? (Integral versus Differential)

There are two forms of the Maxwell equations, one is the differential form, the other is the integral form. Which one is more useful?

Vanadium 50

Staff Emeritus
Science Advisor
Education Advisor
Depends on the problem you are trying to solve.

rude man

Homework Helper
Insights Author
Gold Member
I like the differential form because (1) they apply to every point in space, not just some volume or surface; and (2) with just two purely mathematical relations, to wit, the Stokes and divergence (aka Gauss's) theorems, all the integral relations are immediately derivable from the differential ones.


Science Advisor
Insights Author
Gold Member
The fundamental form of the Maxwell equations is the local, i.e., differential form. A local field theoretical description is in a sense the natural mathematical form for relativistic field theories, and Maxwell's electromagnetism is a paradigmatic example for a relativistic field theory.

Want to reply to this thread?

"Which Form of Maxwell's Equations is More Useful? (Integral versus Differential)" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving