Electrostatic potential and capacitance notes

Electrostatic Potential and capacitance notes

Chapter -2 class 12th Physics notes

Typed Notes of electrostatic potential and capacitance 

Electrostatic potential 

• Electrostatic Potential of a body represents the degree of electrification of the body. It determines the direction of flow of charge between two charged bodies placed in contact with each other. The charge always flows from a body at higher potential to another body at lower potential.  The flow of charge stops as soon as the potential of the two bodies become equal. 

Electrical potential difference- 

Electrostatic potential difference between two points is defined as the amount of work done in moving a unit positive test charge from one point to other point against electrostatic force without any acceleration. Its SI unit is J/C or V (volt). Potential difference is a scalar quantity. 

Electrostatic potential at any point in a region of electrostatic field is the minimum work done in carrying a unit positive charge (without acceleration) from infinity to that point. 

  

 

Important points- 

• Work done by external agent against electrostatic force is taken. 

F ext = - F elec

• Charge should be moved very very slowly so that net electric force at every point is zero. ( Without acceleration or constant velocity) 

• Electric force is a conservative force does the work done by electrostatic force is part independent.  It depends only on initial and final points. 

Electric potential due to a point charge at a distance r from it- 

Potential due to system of charges-

Electric potential at a point due to system of charges is equal to as algebraic sum of the potential at that point due to individual charges. 

The net potential at point P due to system of charges Q1, Q2, Q3,…..Qn Lying at distances r1, r2,r3, ..... rn from point P , 

Net potential at P is equal to sum of potentials due to individual charges.

Vnet = V1 + V2 + V3 +….. +Vn 

Potential at P due to point charge Q1 is  

V1= kQ1/ r1 

Similarly, V2 = kQ2/r2 ,V3= kQ3/r3,…….Vn=kQn/rn 

Then Vnet = k( Q1/r1+ Q2/r2 + Q3/r3 + …… + Qn/rn) 

Electric potential due to a dipole- 

1) On the axis of dipole at distance r from centre of dipole. 

2) On equatorial point of dipole - 

Potential due to continuous charge distribution 

Equipotential surface- 

It is a surface with a constant value of potential at all points on the surface. 

For point charge - concentric spherical shells 

For linear charge - coaxial cylinder 

Properties -

1) Potential difference between any two points on equipotential surface is zero.

2) No work is done by or against electrostatic force in moving a charge over the equipotential surface provided kinetic energy remains constant.

3) Electric field is always perpendicular to equipotential surface at each point of surface.

4) Equipotential surfaces are crowded in a strong electric field region where as they are relatively far apart where the field is weak.

5) Two equipotential surfaces can never intersect each other because if they do so, then at the point of intersection there will be two directions of electric field which is not possible.

6) A charged conductor of any shape under equilibrium is an equipotential surface. if E is not perpendicular then a component of E vector will be Ecostheta on the surface due to which the charge will move.