Relation between Intensity and Potential Difference

Relation between Intensity and Potential Difference

Relation between intensity and potential difference

In order to establish the relation between gravitational intensity and gravitational potential let A and B be two very close points in the gravitational field and let the distance between them be r [Figure]. Let the potential at A = VA and that at B = VB. Since the two points are very close to each other, so we can consider the constant gravitational field there. Let the intensity of the field = F.

Now, amount of work done in bringing a unit mass from point B to point A = Force x distance = Intensity x distance

= F x AB = E x r       [F = E for unit mass]

This is the potential difference between point A and B that is (VA – VB)

so, F x AB = (VA – VB)

or, F = (VA – VB)/AB = (VA – VB)/r

i.e., rate of change of potential difference with distance is called intensity.

If displacement towards the direction of field is AB = dr and potential at point A is VA and that at point B is VB, then VA – VB = – dV

So, F = – dV/dr

This is the relation between gravitational intensity and potential difference.

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