GAUSS LAW
Basic cases where Gauss's law can be performed - single charge particles
-uniformly charge sphere
-uniform line charge
-uniform plane
-linear ; surface ; & volume charge density
GAUSSIAN SURFACE
-OFTEN A SPHERE, CYLINDER OR SOME OTHER SYMMETRICAL FORM
-CAN BE ANY SHAPE, BUT MOST USEFUL SURFACE IS ONE OF THAT MIMICS THE SYMMETRY OF THE PROBLEM AT ONE HAND
-ALWAYS BE A CLOSED SURFACE
Gauss law concept diagram
equations of part 1 & 2 :
If the area is divided into many small elements over the entire Gaussian Surface
1st equation:
Select a gaussian surface around the charge of radius r, with the charge +q at the centre. Therefore, Gauss's law yield a close integral function
2nd equation :
the Gaussian surface is a sphere of area A=4pi
equations of part 3 and 4:
In the limit of continuous surface element, when delta A approaches 0, the expression becomes a closed integral function.
state the Gauss Law for electricity
Gauss Law states that the net number of electric flux through any closed surface is proportional to the total electric charge enclosed by this surface.
Non-conducting solid sphere
1) Regions inside the distribution (0<r<R)
Gauss law, phi=E.dA=q/e
net charge enclosed by the Gaussion surface =
q= Rho x V
= Rho x (4pi r^3/3)
= (4pi r^3/3 x Rho
By substituting the charge q into the Gauss law equation above :
E=( Rho x r ) /3e
2) Outside the Charge Distribution, (r>R)
Select a spherical Gaussian surface with radius (r>R).
q= 4pi x R^3 x Rho/3
E= (rho x R^3 ) / 3 epsilon r^2
Electric potential
Work done :
W=F.s
F=force
S=displacement
work-energy theorem
W=KE=1/2mv^2
Electric potential energy for a system of point charges
Electric potential for multiple point of charges
electrostatic potential energy for a positively charge conducting sphere as a function of distance, r
Coulomb's law
definition
Electric potential of a point charge
V=kQ/r
Coulomb's law state that the electrical force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
F=kq1q2/r^2
k=coulomb's constant
q=charges
r=distance of seperations
unit of charge:coulomb, C
k=8.99x10^9 Nm^2/C^2
e=1.602x10^-19C
ELECTROSTATICS
GAUSS LAW
ELECTRIC POTENTIAL
COULOMB'S LAW
Coulomb's law is applicable only to electric fields