Download - Lectures on Electromagnetic theory
Lectures on
Electromagnetic theory
PH 2151
Lecture 2
(The three coordinate systems)
Prof. Salwa Saad Mohamed
The cartesian coordinate system
The coordinates are x y z
The position vector r=x 饾憥饾懃 +y 饾憥饾懄 +z 饾憥饾懅.
The perpendicular unit vectors are 饾憥饾懃,
饾憥饾懄, 饾憥饾懅.
The cartesian coordinate system
The displacement element
dl = dx 饾憥饾懃 +dy 饾憥饾懄 + dz 饾憥饾懅
The volume element
dv= dxdydz
Circular cylindrical coordinate system
The coordinates are 蟻, 蠁,z
The unit vectors are 饾拏蟻 , 饾拏蠁, 饾拏饾懅.
The displacement element dl = d蟻 饾拏蟻+蟻d蠁 饾拏蠁 + dz 饾拏饾懅
The volume element dv= d蟻 蟻d蠁 dz
Circular cylindrical coordinate system
The relation of the variables in rectangular and cylindrical coordinate systems and vise versa is :
Circular cylindrical coordinate system
The spherical coordinate system
The three coordinates are r, , 肖
The unit vectors are 饾悮饾憻, 饾悮, 饾悮肖.
The displacement element dl= dr 饾悮饾憻+rd 饾悮+ rsin 饾憫肖 饾悮肖
The volume element dv= dr rd r sin d蠁
The spherical coordinate system
The relation of the variables in rectangular and spherical coordinate systems and vise versa is :
The Spherical coordinate system
Problems: 1. Find the vector directed from the point (10,3/4,/6) to the
point ( 5,/4,).
2. Find the distance between the points (2, 6, 0) & (1, , 2).
3. Using the spherical coordinate, obtain the volume between
1 r 2 m , o /2 and o 蠁 /2.
4. Transform the vector A= y饾憥饾懃 +x 饾憥饾懄 +饾懃2
(饾懃2+饾懄2饾憥饾懅 into
cylindrical coordinate system .
5. Use the cylindrical coordinates to find the surface area of
cylinder with radius a and height h.
