1. By Prof. Hitesh Dholakiya
Stokes Theorem
Electromagnetics
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Engineering Funda Android App Electromagnetic Theory YT Playlist
2. Basics of Stokes Theorem
Statement of Stokes Theorem
Proof of Stokes Theorem
Physical significance of Stokes Theorem
Outlines of Session
Use of Stokes Theorem
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Engineering Funda Android App Electromagnetic Theory YT Playlist
3. Basics of Stokes Theorem
❖ Stokes theorem explains relationship in between line integration and surface
integration.
❖ Stokes theorem is based on curl of function.
❖ Curl of function explains rotation of body at different position, means torque at the
position.
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Engineering Funda Android App Electromagnetic Theory YT Playlist
4. Function of Stokes Theorem
❖ Mathematically Stokes theorem expressed as
ර 𝑃. 𝑑𝑙 = න ∇ × 𝑃 𝑑𝑆
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5. Proof of Stokes Theorem
❖ Curl of any function 𝑷 can be calculated by
❖ So further calculation can be done by
❖ So for total length
𝐶𝑢𝑟𝑙 𝑃 = ∇ × 𝑃 = lim
∆𝑆→0
ׯ 𝑃 𝑑𝑙
∆𝑆
⇒ lim
∆𝑆→0
∇ × 𝑃 ∆𝑆 = lim
∆𝑆→0
ර 𝑃 𝑑𝑙
ර 𝑃. 𝑑𝑙 = න ∇ × 𝑃 𝑑𝑆
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7. Use of Stokes Theorem
❖ It is used in applications of fluid mechanics
❖ It is used to understand electromagnetics
❖ It is used to understand flaw of fields (e.g. Gravitational fields, Electric field, Magnetic
field etc)
❖ It is used in aerodynamics.
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