Stokes theorem explains the relationship between line integration and surface integration. It is based on the curl of a function, which describes the rotation of a body at different positions or torque. Stokes theorem mathematically equates the line integral of a vector field P around a closed curve C to the surface integral of the curl of P over any surface S bounded by C. It has various applications in fields like fluid mechanics, electromagnetics, and aerodynamics to understand the flow of fields.

1. By Prof. Hitesh Dholakiya
Stokes Theorem
Electromagnetics
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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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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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6. Physical significance of Stokes Theorem
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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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