Charge Density and conductor

Charge density

Linear charge density
λ=Q/L=dQ/dL

Surface charge density
σ=Q/A=dQ/dA

Volume charge density
ρ=Q/V=dQ/dV

Electrostatics in Conducter
1.E=0 inside the conducter
2. All charge resides on the outer surface of the conducter
3.Electric at the surface is Perpendicular to the surface

Electric Field

Electric field-The region around a particular charge in which its electrical effects can be observed is called the electric field of the charge

-Electric field has its own existence and is present even if there is no charge to experience the electric force.

Electric field Intensity:

E=F/q0

Where F is the electric force experience by the test charge q0 at this point.
It is the vector quantity

Some point to note on this1.Electric field lines extend away from the positive charge and towards thge negative charges
2. Electric field produces the force so if a charge q is placed in the electric field E the force experience by the charge is
F=qE
3 Principle of superposition also applies to electric field
so E=E1+E2+E3+E4+......

Electric field intensity due to point charge
E=KQr/r2
Where r is the distance from the point charge and r is the unit vector along the direction from source to point.

Some useful Formule
Electric field for the Uniformly charged ring

E=KQx/(r2+x2)3/2
Where x is the distance from the center of the ring
At x=0
E=0
Electric Field due to uniformly charged disc
E=(σ/2ε0)(1- x/(√R2+x2))
σ=Surface charge density of the disc
At x=0
E=σ/2ε0

Electric Field Intensity due to Infinite sheet of the charge
E=σ/2ε0
σ=Surface charge density of the sheet

Electric Charges and Coulumb's Law

- Charges are of two types
(a) positive charge
(b) negative charge

- like charges repel each other and unlike charges attract each other.

-Properties of charge
1. quantisation :- q=ne where n=0,۫, ........ and e is charge of an electron.
3. conservation :- total charge of an isolated system is constant

-Coulumb's law
The mutual electrostatic force between the charges q1 and q2 seperated by a distance r is given by
Force on the charge q1
F1=Kq1q2r12/r2
where r12 is the unit vector in the direction from q2 to q1
similarly force on charge q2 is
F2=Kq1q2r21/r2
where r21 is the unit vector in the direction from q1 to q2
F1+F2=0
If there are more than 2 charges present in the system then force acting on any charges is vector sum of the couloumb force from each of the other charges.This is called principle of superposition
Mathematically
Let q1,q2,q3......qn
charges are present in the system
Then Force on charge q1
F=Kq1q2r12/r122+Kq1q3r13/r132+Kq1q4r14/r142....Kq1qnr1n/r1n2

Similarly for the other charges...

Important point to note on this
1. The force with which two charges interact is not changed by the presence of the other charges
2. Net force on any charge
F=F1+F1+F1+F1....