Question

Derive the differential expression between between electric field and electric potential

Answer 1

Electric field can exist only if there is a difference in potential. Potential, however high, if it is equal at all points, there will be no electric field. This is what happens inside a charged hollow sphere. Inside the sphere, there is potential, but no potential difference, hence no field.

Thus, in general Electric field is defined as negative space derivative of potential.

Considering one dimensional case for simplicity,

E = - dV/dx

Or E= - (gradient of potential)

(-) sign indicates that field is directed from higher potential to lower potential.

Answer 2

heyaa!!

I think this helpss!! :-)

here's ur ans:-

Electric Potential and Electric Field. ... Thus, the above formula is saying that the -component of the electric field at a given point in space is equal to minus the local gradient of the electric potential in the -direction.

Hence electric field is the negative gradient of the scalar potential. The negative sign came as a result because the potential difference is the work done per unit charge against the electrostatic force to move a charge from a to b. However, this equation is valid only for static electrostatic fields.

Electric potential is simply the work done per unit charge to move it from one potential to another potential within the electric field. The difference between two different equipotentials is the potential difference or voltage difference.

I've added some extra points....