equipotential surface , electric potential energy and electric potential

                Equipotential       surface               

what is an equipotential surface ?

 give an example. 

equipotential is made up of two words equi and potential . equi means equal or same  
potential means capacity do work due to any particular charge. 
In simple ways it can be defined as those surface where electric potential remains same  or equal is called equipotential surface. 
example -: surface of conductor .

key point regarding equipotential surface

👉Electric field is directed perpendicular to the equipotential surface . 
👉The component of electric field along equipotential surface is zero .
👉 In moving charge on equipotential surface work done is zero . 

How the component of electric field along equipotential surface is zero ?

As we know , cos 90 (degree) = 0

so component of electric field (E ) is also 0 . 

How the work done by moving charge on equipotential surface is 0 ?

For equipotential surface  , potential at any point of surface is equal . so let the potential at point A is vA and potential at B point is VB. 
so , VA = VB   ----------   (equation 1) 
now the work done the external agent 
=  q * (VB  -  VA  )
 = q *  (  0  )   (  VA = VB )
 = 0      

                                                   

prove that electric field is directed perpendicular to the equipotential surface ?  

 

what is equipotential surface for point charge ?

for a single point charge equipotential surface is in spherical shape. 
Here Arrow show the direction of electric field which is always perpendicular to the surface , as show in the diagram. 

what is equipotential surface for a uniform electric field ?

for uniform electric field equipotential surface is planes. 

what is electrostatic potential energy ?  

Electrostatics potential energy is stored form of energy due to position or configuration of charge particle 
❋ Along tendency potential energy decreases and kinetic energy increases . 
❋Away from tendency potential energy increases and kinetic energy decreases . 
❋potential energy is a state function.
❋Having no absolute value. 
❋depend on initial and final position . 
❋Independent of path. 

change in electrostatics potential energy between point A and B  

change in electrostatic potential energy between two point A and B is defined as negative of work done by electrostatics force taking charge particle from A to B . 

 

 

change in potential energy between point A and B  

change in potential energy between two point A and B is defined as the +ve of workdone by external agent taking charge particle from A to B in such a way that no accleration is produced . 

what is Electric potential ?

❋Electric potential is capacity to do work due to particular charge .
❋Electric potential is state function . It has no absolute value .
❋ It is Indpendent of path . 
❋It depend on initial and final position .
❋Electric potential decreases in the direction of electric field . 
❋Electric potential remain constant perpendicular to the electric field . 
❋Electric potential increase in the direction opposite of electric field. 

what  is potential difference ?  

potential difference between two point A and B is defined as negative of work done by by electric field taking charge particle from A  to B . 

 

 Here E vector represent electric field . 

why we can't define electric potential or potential at a point ?

we can't define electric potential and potential at a point because it a state function . state function mainly depend upon initial and final position . 

Note -: we can calculate electric potential or potential at a point by taking the reference level . At the reference level electric potential and potential energy is taken to be  0 .

Generally reference level is taken at infinity because at infinity electric field and electric force is 0. 

What is conservative force ? 

❋Those force for which work done depend up on initial and final position is called as conservative force .
❋work  done by conservative force is independent of path 
❋work done by conservative force in round trip is zero (0) 
❋direction of conservative force is independent of direction of  motion . 
❋Electrostatics force is conservative force .

 

   w1 = w2 = w3 

 

This represent the work done  in the round trip . 

  Electric potential due to a single charge   

electric field due to a single charge is 

Electrostatics potential energy of a  system of two charge 

Electrostatics potential due to charge (q1) at a distance r . 

here v(r) is the potential at a distance of r . 
q1 and q2 are the two charges which is placed at a distance of r . 
ub  = potential energy at a distance b 
ua = potential energy at a distance a 
u(infinity) = potential at a distance of infinity 

How do you find the electric potential of  a dipole moment  ?           

  consider an electric dipole having charge -q and +q charge separated by distance 2l . To find the electric potential at a distance r from the centre which makes an angle Ө with the dipole axis . 
then draw perpendicular from A and B on line of these perpendicular are AA' and BB'  

For a right angle triangle OAA' 

   The electric potential due to a single charge is independent of direction and for an electric dipole is 
  so ,  V is directly proportional to cos Ө  . 

👉For a single charge electric potential is inversely proportional to distance from charge and for an electric dipole inversely proportional to square of the distance from the centre . 

I hope this will helpful for you .

Thank you for reading my post 

please comment and share so that many one get benefited.
Any doubt regarding this post is always welcome .
 so  kindly ask your question (doubt) in the comment section.

suman kumar

Thank you !

sharing icon is down below👇