Question

What is the relation between gravitational intensity and gravitational potential at a point?

Answer 1

Answer:

Gravitational intensity at a point is equal to negative value of gradient of potential at that point, i.e., I=-dV/dr.

Answer 2

Relation between Gravitational Intensity & Gravitational Potential :

First of all, let's define the terms :

• Gravitational Field Intensity is a the strength of gravitational force at a particular point per unit mass with respect to a reference.

• Gravitational Potential is a scalar quantity representing the amount of work done to move a unit mass from infinity to a particular point in the gravitational field.

Gravitational field intensity is a vector quantity where is gravitational potential is a scalar quantity.

Mathematically, they are related as :

$\boxed{ \displaystyle \: dV = - \int E \: dr}$

It can also be related in term of partial derivates as:

$\boxed{E = - \dfrac{ \partial V}{ \partial \: r} }$

Hope It Helps.