Physics Formula electric charges and fields

Physics Formula electric charges and fields

Physics Formula – 1

Apply Coulomb’s law

q₁ = first charge

q₂ = Second charge

r = distance between both charge

ε₀= permittivity of free space

1/4πε0 = 9 x 10⁹ Nm²C^-2

Coulomb’s law

Physics Formula – 2

Coulomb’s force law between two point charges q₁ and q₂ located at r₁ and r₂ is then expressed as

Coulomb’s force law between two point charges

Physics Formula – 3

Thus the total force F1 on q1 due to the two charges q2 and q3 is given as

total force F1 on q1 due to the two charges q2 and q3

Physics Formula – 4

Coulomb’s law of resultant force 

Coulomb’s law of resultant force

Physics Formula – 5

The electric field produced by the charge Q at a point r is given as

electric field produced by the charge Q at a point r

Physics Formula – 6

Vactor Force F exerted by a charge Q on a charge q 

Vactor Force F exerted by a charge Q on a charge q

Physics Formula – 7

The electric field E at r due to the system of charges is 

electric field E at r due to the system of charges

Physics Formula – 8

The total flux φ through a surface S is

φ ≈ Σ E.ΔS

Physics Formula – 9

the electric field of a dipole at large distances takes simple forms:

At a point on the dipole axis

electric field of a dipole at a point on the dipole axis

At a point on the equatorial plane

electric field of a dipole a point on the equatorial plane

Physics Formula – 10

Surface charge density σ at the area element by 

Surface charge density σ at the area element

Physics Formula – 11

The linear charge density of a wire is defined by

linear charge density of a wire

Physics Formula – 12

The volume charge density (sometimes simply called charge density) is defined as

volume charge density

Physics Formula – 13

Electric field due to the charge ρΔV is given by Coulomb’s law:

Electric field due to the charge ρΔV is given by Coulomb’s law

Physics Formula – 14

The total electric field due to the charge distribution is obtained by summing over electric fields due to different volume elements:

total electric field due to the charge distribution

Physics Formula – 15

Total flux through a sphere of radius r, which encloses a point charge q at its centre.

Total flux through a sphere of radius r

Physics Formula – 16

Electric flux through a closed surface S

∆ φ1 = q/ε0

Physics Formula – 17

Flux through the Gaussian surface 

Flux through the Gaussian surface

Physics Formula – 18

Field due to a uniformly charged infinite plane sheet 

Field due to a uniformly charged infinite plane sheet

n is a unit vector normal to the plane and going away from it

Physics Formula – 19

Field outside the shell

Field outside the shell

Field inside the shell

E=0