A force `vecF=2xhat(j)` newton acts in a region where a particle moves annticlockwise in a square loop of 2m in x`-`y plane as shown in figure . Calculate the total amount of work done. Is this force a conservative force or a non-conservative force?

Explanation

Here, `vecF=2xhat(j)` newton
Total work done in moving the particle
`W=int_(ABCDA) vecF.dvec(x)`
`=int_(0)^(2)(2xhat(j)).(dx)i+int_(0)^(2)(2xhat(j)).(dx)hat(j)`
`+int_(2)^(0)(2xhat(j)).dx(-hat(i))+int_(2)^(0)(2xhat(j)).dx(-hat(j))`
`=0+2[(x^(2))/(2)]_(0)^(2)+0-2[(x^(2))/(2)]_(0)^(2)`
`=4-(0-4)=8J`
As work done by the force around a round trip is not zero, therefore, the force must be non-conservative.