If gravitational field is given by `E -x hat(i) - 2 y^(2) hat(j)`. When gravitational potential is zero ar (0,0) find potential cat (2,1)

Explanation

Given, gravitational field
`E=-xhat(i)-2y^(2)hat(j),E_(x),=-x and E_(y)=-2y^(2)`
As we know that,
`V(r_(2))-V(r_(1))=-int_(r_(1))^(r_(2))E.dr`
`rArrV(2,1)-V(0,0)=0[int_(0)^(2)E_(x)dx+int_(0)^(1)E_(y)dy]`
`=-[int_(0)^(2)-xdx+int_(0)^(1)-2y^(2)dy]`
`=+[((x^(2))/(2))_(0)^(2)+(y^(2))_(0)^(1)]=[(4)/(2)+1]=3` unit
`rArr V(2,0)=3+(0,0)=3+0=3` unit