# Electric Charges And Fields

Coulomb’s Law:

Coulomb’s law states that the magnitude of the Electrostatics force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distances between them.

F=k q1 q2 / r2

where

F = force on one charge by the other

k= Coulomb constant (8.98× 109 N m2 C−2)

q1 = charge

q2= charge

r= distance

If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different sign, the force between them is attractive.

Electric Field:

E = F/q

= kq / r2

where

F= field

q = charge

k= Coulomb constant (8.98× 109 N m2 C−2)

Electric field lines radiate outward from positive charges.The electric field is zero inside a conductor.

Relationship of k to ε0

Coulomb’s constant is k, a proportionality factor also called the electric force constant or electrostatic constant,

k = 1 / (4 π ε0)

where

k = Coulomb constant (8.98× 109 N m2 C−2)

ε0 = permittivity of free space (8.85× 10-12)

Electric Field due to an Infinite Line of Charge:

E = 2kλ / r

where

λ = charge per unit length

r = distance

k = Coulomb constant (8.98× 109 N m2 C−2)

Electric Field due to an infinite sheet:

E=σ/ 2 ε0

where

σ = charge per unit area

ε0 = permittivity of free space (8.85× 10-12)

Electric Field inside a spherical shell

E=kqr / R3

where

r = distance from center of sphere to the charge

q = charge

R = radius of the sphere

Electric Field outside a spherical shell

E=kq / r2

where

r = distance from center of sphere to the charge

q = charge