Question

If gravitational potential is `V = xy^(2)`, find the gravitational field at `(2,1)`

Answer 1

Given, `V = xy^(2)`
Electric fieldin x-direction
`E_(x)=(-delV)/(delx)=(-del)/(delx)(xy^(2))=-y^(2)`
Electric field in y-direction
`E_(y)=(-delV)/(dely)=(-del)/(dely)(xy^(2))=-2yx`
`:. E=E_(x)hat(i)+E_(y)hat(j)=(-y^(2))hat(i)+(-2xy)hat(j)`
`:. E(x=2,y=1)=(1)^(2)hat(i)+(-2xx2xx1)hat(j)`
`rArr |E|=sqrt((-1)^(2)+(-4)^(2))=sqrt(17)` unit