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4 Questions around this concept.
What is the relationship between gravitational field strength and gravitational potential?
Gravitational field and potential are related as
Where E is Gravitational field
And V is Gravitational potential
And r is the position vector
And Negative sign indicates that in the direction of intensity the potential decreases.
Then
Proof-
Let gravitational field at a point r due to a given mass distribution is E.
If a test mass m is placed inside a uniform gravitational field E.
Then force on a particle m when it is at r is as shown in figure
As the particle is displaced from r to r + dr the
work done by the gravitational force on it is
The change in potential energy during this
displacement is
And we know that Relation between Potential and Potential energy
As
So
Integrating between r1, and r2
We get
If r1=r0, is taken at the reference point, V(r0) = 0.
Then the potential V(r2=r) at any point r is
in Cartesian coordinates, we can write
Then
So
If y and z remain constant, dy = dz = 0
Thus
Similarly
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