LINES OF FORCE
•The lines of force gives the direction of the electric field
at any point
•In complex field where the curves of lines exist the
direction is mentioned by tangents of the electric field.
•The Line of force originate on +ve charge and terminate
on –ve charge
•The line of force are drawn so that the number of lines
per unit cross sectional area is proportional to the
magnitude of the electric field.
THE ELECTRIC FIELD OF CONTINUOUS
CHARGE DISTRIBUTION.
Even though electric charge is quantized, a collection of a
large number of elementary charges can be regarded as a
continuous charge distribution.
•Divide this charge distribution into infinitesimal element dq.
•Each element of charge establishes a field dE at a point P.
•Resultant field E can be find out by adding the field
contributions due to all the charge elements..
E=  dE
In Cartesian Coordinates
Ex =  dEx
Ey =  dEy
Ex =  dEz
dE = 1/40 dq/r2
CHARGE ELEMENT dq DUE TO LINEAR
CHARGE DISTRIBUTION
Continuous distribution of charge is described by its charge
density..
In linear charge distribution, such as a thin filament onto which
charge has been placed, an arbitrary element of length ds carries
a charge dq is given by .
dq =  ds
Where  is linear charge density and is equal to the total charge
q on the object divided by its total length L, where charge
distribution is uniform.
Here.
dq = q/L ds (uniform linear charge)
CHARGE ELEMENT dq DUE TO SURFACE
DISTRIBUTION
In surface distribution, an arbitrary element of area dA carries a
charge dq is given by .
dq =  dA
Where  is surface charge density and is equal to the total
charge q on the object divided by its total area A, where charge
distribution is uniform.
dq=q/A dA (Uniform surface charge)
CHARGE ELEMENT dq DUE TO VOLUME
DISTRIBUTION
In volume distribution, an arbitrary element of volume dV
carries a charge dq is given by .
dq = dV
Where rho ( ) is volume charge density and is equal to the
total charge q on the object divided by its total volume V,
where charge distribution is uniform.
dq=q/V dV (Uniform volume charge)