This is a maths ppt on use of vector suface integral on gravitational force,electrostatics gauss law and pressure force.

1. CREATED BY-
KARISHMA YADAV(57)
RAHUL YADAV (58)
SAURABH YADAV (59)
SHUBHAM YADAV (60)

2. INTRODUCTION
The vector surface integral is a
powerful tool in physics that is
used to calculate various physical
quantities.
It involves integrating the product of
a vector field and a surface element
vector over a surface of interest.

3. Gravitational force
The vector surface integral can be
used to calculate the total
gravitational force on a surface due
to a distribution of masses.
The force is given by the product of
the gravitational constant, the mass
density, and the surface element
vector integrated over the surface.

4. PRESSURE FORCE
The vector surface integral can also
be used to calculate the total pressure
force on a surface due to a fluid flow.
The force is given by the product of the
pressure, the surface area vector, and
the unit normal vector integrated over
the surface.

5. Gauss's Law in Electrostatics
In electrostatics, the vector surface integral
is used to calculate Gauss's law, which
relates the electric field to the charge
distribution in a closed surface.
The law states that the electric flux through
a closed surface is equal to the total charge
enclosed within the surface divided by the
permittivity of free space.
The vector surface integral of the electric
field over the closed surface is equal to the
total charge enclosed within the surface
divided by the permittivity of free space.

6. Calculating Pressure Force
To calculate the gravitational force
on a surface due to a distribution of
masses, we integrate the product of
the gravitational constant, the mass
density, and the surface element
vector over the surface.
The resulting force vector gives us
the total gravitational force on the
surface.

7. Calculating Pressure Force
To calculate the pressure force on a
surface due to a fluid flow, we integrate
the product of the pressure, the surface
area vector, and the unit normal vector
over the surface.
The resulting force vector gives us the
total pressure force on the surface.

8. Calculating Gauss's Law in
Electrostatics
To calculate Gauss's law in
electrostatics, we integrate the
electric field over a closed surface
and equate it to the total charge
enclosed within the surface
divided by the permittivity of free
space.
The resulting equation gives us a
relationship between the electric
field and the charge distribution in
a closed surface.

9. CONCLUSION
The vector surface integral is a
useful tool in physics that can be
used to calculate a wide range of
physical quantities in various fields.
Its application in gravitational force,
pressure force, and electrostatics is
just a few examples of its versatility
and importance in physics.