Physics
If'd' represents the distance, then the relation between electric intensity and potential difference is given by........
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Answer:
Relation between Electric field and potential
The relationship between electric field E and scalar potential φ is given as
E=−∇φ
where ∇≡gradient operator.
I am unable to understand from this - sign comes.
It is worthy to quote from Purcell:
The minus sign came in because the electric field points from a region of positive terminal toward a region of negative terminal, whereas the vector ∇φ is defined to so that it points in the direction of increasing φ.
The crux of this quote is that the electric field E points in the direction opposite to the direction of increasing scalar potential φ.
Which step I have done wrong?
Remember, change in potential energy U is given as
U(x)−U(x0)=−∫xx0F(x)dx.
So, your approach should be the work done against the electric field by an external agent in carrying the charge from point A to B and that would imply the work would be given by negative component of the electric field in the direction of motion .