Derive the relation between electric field and electric potential.

Explanation

Detailed Answer :
Relatioon between electric field and electric potential .
Say .A and B are two point in an uniform electric field.Potential at point B is greater than the potential at point A .

If +`Q_(0)` Amount of charged is moved between the points and `W_(AB)` is the work done ,the work done per unit charge `(V_(B)-V_(A))`
A charge +`Q_(0)` in an electric field E will experience a force `Q_(o)E` in the direction of the field .
An external agent must apply same amount of force of move the charge from A to B
`F_(EXT)=Q_(0)E`
Work done =`W_(AB)=F_(EXT)xxAB`
`W_(AB)=Q_(0)ExxAB` ..........(ii)
Comparing equation (i) and (ii) `Q_(0)ExxAB=(V_(B)-V_(A))Q_(0)`
or ,`E=(V_(B)-V_(A))/(AB)` The above results shows that if the potential difference between two plates separated by a distance l,then assuming an uniform field E between the two plates ,`E=(V)/(l)`