Electric flux 

1. Electric flux (Φ_E) linked with a surface (flat or curved) gives us an idea of the total number of electric field lines passing normally through that surface.

2. Electric flux is defined as the surface integral of the electric field inked with that surface i.e.

Here θ is the angle between electric field vector & area vector ( i.e. an area vector conventionally directed normally outwards to the area under consideration).

3. SI unit of flux: Weber (Wb)

4. CGS unit of flux: Maxwell (Mx)

5. Conversion: 1Wb = 10 ⁸ Maxwell = 1Vm

6. Being dot product, electric flux is a scalar quantity.

7. Maximum value of flux = ± E S

8. Minimum value of flux = 0 (when θ = π/2)

9. If θ is acute flux is + ve & called leaving.

10. If θ is obtuse flux is – ve & called entering.

Electric dipole in uniform electric field

Consider an electric dipole in a region of uniform electric field

1. Net force on the dipole for any position is zero.

2. Torque acting on the dipole is .

3. Torque acts except for the positions when the dipole moment vector & electric field vector are collinear.

4. Total work done by us in rotating the dipole in a uniform electric field is from angle θ₁ to θ₂ is

W = pE (cos θ₁ – cos θ₂)

5. The potential energy of an electric dipole placed in a uniform electric field is

6. A dipole placed in a non uniform electric field experiences both force and torque.

7. Force on a dipole placed in shown non uniform electric field is