Question

The gravitational potential due to a mass distribution is `V=A/sqrt(x^2+a^2)`. Find the gravitational field.

Answer 1

V=A/sqrt(x^2+a^2)=A(x^2+a^2)^(-1/2)`
If the gravitatioN/Al field is E.
`E_x=(delV)/(delx)=-A(-1/2)(x^2+a^2)^(-3/2)(2x)`
=(Ax)/((x^2+a^2)^(3/2))`
`E_y=-(delV)/(dely)=0 and E_z=-(delV)/(delZ)=0`
the gravitatioN/Al field is `(Ax)/((x^2+a^2)^(3/2))` in the x direction.