Factors deciding flux

Electric flux depends only upon

(a) the number of charges enclosed by Gaussian surface

(b) nature of charges enclosed by Gaussian surface

(c) nature of the medium. & is independent of

(d) size of surface

(e) distance between charges inside the surface

(f) distribution of charges.

Diagram explains that the net electric flux through each surface is the same irrespective of the shapes of the closed surfaces surrounding a charge q.

Diagram explains that the no net flux is linked with the closed surface if a point charge is located outside a closed surface as in this case the number of lines entering the surface equals the number leaving the surface.

Diagram explains that the net electric flux through any closed surface depends only on the charge inside that surface. The net flux through surface S_A is q₁/e₀, the net flux through surface S_B is and net flux through surface S_C is zero.

^Numerical & unit

The magnitude of a quantity doesn’t change with the change of unit. i.e. numerical & unit of a physical quantity are inversely proportional.

Potential energy of point charges

1. For a system of two point charges

2. For a system of three point charges

3.

4. For a stable system U is minimum, its first derivative w.r.t. position (= – F) is zero & its second derivative w.r.t. position is +ve.

Electrostatic force

Electrostatic force has following properties

1. Force on any charged particle situated in its electrostatic electric field is given by

  [Called electrostatic Lorentz force

2. This force is independent of direction or amount of their velocity.

3. It acts in the direction of field on a positive charge & acts opposite to the direction of field on a negative charge.

4. Acceleration of a charge particle due to force exerted by the electric field using NSL is

5. Both +ve & -ve charge particle when accelerate under this force always moves in the direction of decreasing potential energy, mathematically this situation is expressed as

Called law of conservative force.

6. Dropping integral & vector sings & rearranging the above relation can be expressed as  i.e. a conservative force is equal to negative of potential energy gradient.

7. Loss of potential energy of a system implies equal amount of gain in the KE so that the mechanical energy (i.e. K + U) of the system moving in electrostatic electric field is always conserved (i.e. constant). This is why electrostatic force is called conservative.