Application of maths in pysiscs. Here is complete Physics has many applications in everyday life. The importance of physics is highlighted by the many applications of physics in our daily lives. Physics is a branch of science that deals with matter, its nature and properties, and deals with heat, mechanics, light, electricity, magnetism, the shape of atoms and sound.

1. APPLICATION OF MATHS IN PHYSICS

2. Group
Members Name
1. Haider Ali 22101001-062
2. Rasikh Attique 22101001-058
3. Ahmer Sheraz 22101001-043
4. Turab Zaidi 22101001-061
5. Manan Ijaz 22101001-042

3. TOPIC
STOKE’S THEOREM

4. Content….
Where Maths meet Physics ?
Introduction.
Stokes theorem w.r.t to Maths.
Stokes theorem w.r.t to Physics.
• Defination of Stokes Theorem.
• Derivation.
• Conclusion.

5. Where Math meet
Physics ?
Math and physics are two closely
connected fields. For physicists, math is
a tool used to answer questions.
For example:
Calculus to help describe motion. For
mathematicians, physics can be a
source of inspiration, with theoretical
concepts such as general relativity
and Quantum theory providing an
impetus for mathematicians to develop
new tools.

6. Introduction  In differential geometry Stokes'
theorem is a statement about
integration of deferential form which
generalizes several theorems
from vector calculus.
 It is named after Sir George Gabriel
Stokes(1819–1903), although the first
known statement of the theorem is
by William Thomson(Lord Kelvin) and
appears in a letter of his to Stokes
in July 1850.
 In 1854, he asked his students to prove
the theorem on an examination.

7. Stokes theorem w.r.t Maths
Defination:
The Stoke’s theorem states that “The surface integral of the curl of a function over a
surface bounded by a closed path is equal to the line integral of a particular vector
function around that surface.
𝐹 ⋅ 𝑑𝑟 =
𝑆
curl 𝐹 ⋅ ⅆ𝑆
Use of Stoke’s theorem:
• To turn surface integrals through a vector field into line integrals.
• A difficult surface integral into an easier line integral.

8. Where,
C = A closed curve.
S = Any surface bounded by C.
F = A vector field.

9. Stoke’s Theorem w.r.t Physics
Defination :
According to this theorem, the line integral of a vector field A vector around any
integral of the curl of A vector taken over any surface S of which the curve is a

10. Stokes theorem Proof:
Let A vector be the vector field acting on the surface enclosed by closed curve C. Then the line integral of vector A
vector along a closed curve is given by
where dl vector is the length of a small element of the path…..

11. Now let us divide the area enclosed by the closed curve C into two equal parts by drawing a line ab as shown in fig. We
have now two closed curves C1 and C2.
Therefore, the line integral of vector A vector along a closed curve C can be written as
If the area enclosed by the curve C is divided into a large number of small areas such as dS1, dS2, dS3………………
dSn bounded by the curves C1, C2……………Cn as.....

12. According to the definition of curl.
Put this value in (2), we get
Now we convert 𝛴 − 𝑎𝑛𝑑 new equation is
where, dSn is the surface area in the case under consideration

13. Hence eqn. (4) can be written as
Curl A Vector according to definition is equal to the change in integral vector ∇.

14. Application of Stoke’s Theorem
• Basic use of stokes theorem arises when dealing with the calculations in the areas of
the magnetic field.
• Basically Stokes theorem is a 3-D version of the Green’s theorem.
• Stokes' theorem is also used for the interpretation of curl of a vector field. This
theorem is quite often used in physics, especially in electromagnetism.
• Stokes' theorem and its generalized form are very important in finding line integral of
some particular curve and also in determining the curl of a bounded surface.
• Water turbines and cyclones may be an example of Stokes and Green's theorem.

15. THANK YOU