Question

derive
relation between electric field and electric potential?​

Answer 1

This is a simple derivation.

By definition, we know that:

W=q(Vfinal−Vinitial)W=q(Vfinal−Vinitial)

W=q((V+dV)−V)W=q((V+dV)−V)

W=qdVW=qdV

And

W=F→external⋅dr→W=F→external⋅dr→

Where,

F→external=−qE→F→external=−qE→

Here negative sign is due to the fact that the applied force is in the opposite direction to the force experienced by the particle by the electric field.

For simplicity, let E→=Ei^E→=Ei^ and dr→=dri^dr→=dri^ where EE and drdr are components in the i^i^ direction.

Therefore,

W=−qEi^⋅dri^=−qEdrW=−qEi^⋅dri^=−qEdr

But,

W=qdVW=qdV

Therefore from above two equations, we get,

E=−dVdrE=−dVdr

Hope it helps.