Question

Gravitational potential in x-y plan varies with x and y coordinates as V = x^(2)y+2xy Find gravitational field strength E.

Answer 1

gravitational field strength would be -(2xy + 2y)i - (x² + 2x) j

Given, Gravitational potential in x - y plane varies with x and y co-ordinates as V = x²y + 2xy

we know,

$\nabla E=-\frac{\delta}{\delta x}\nabla V$

$\nabla E=-\left(\frac{\delta}{\delta x}+\frac{\delta}{\delta y} +\frac{\delta}{\delta z}\right)V$

now δV/dx = δ(x²y + 2xy)/δx = 2xy + 2y

δV/δy = δ(x²y + 2xy)/δy = x² + 2x

δV/δz = δ(x²y + 2xy)/δz = 0

gravitational field strength, E = -[(2xy + 2y)i + (x² + 2x) j]

= -(2xy + 2y)i - (x² + 2x) j

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