The electric field exists if and only if there is a electric potential difference. If the charge is uniform at all points, however high the electric potential is, there will not be any electric field. Thus, the relation between electric field and electric potential can be generally expressed as – “Electric field is the negative space derivative of electric potential.”
Electric Field And Electric Potential
The relation between Electric field and electric potential is mathematically given by-
| E=−dV dx |
Where,
E is the Electric field.
V is the electric potential.
dx is the path length.
– Sign is the electric gradient
Direction of Electric Field
- If the field is directed from lower potential to higher then the direction is taken to be positive.
- If the field is directed from higher potential to lower potential then the direction is taken as negative.
Electric Field And Electric Potential Relation
| Test charge | Formula | Electric gradient |
| Positive | wq0=∫abE→.dl→=Vb−Va | Higher as you go closer towards test charge. |
| Negative | wq0=∫abE→.dl→=Va − Vb | Higher as you go move away from test charge. |
| Equipotential surfac | wq0=∫abE→.dl→=0 | Electric potential is perpendicular to Electric field lines. |