Find the potential difference between point A and B in an electric field `barE=(2hati+3hatj+4hatk)NC^(-1)` where `barr_(A)=(hati+2hatj+hatk)m and barr_(B)=(2hati+hatj-2hatk)m`.

Explanation

We know that `dV= -barE.dbarr`
`V_(AB)=V_(A)-V_(B) = -int_(A)^(B) barE.dbarr`
`= -int_("(2,1,-2)")^("(1,-2,1)") (2hati+3hatj+4hatk).(dxhati+dyhatj+dzhatk)`
`=-int_("(2,1,-2)")^("(1,-2,1)") (2dx+3dy+4dz)`
`= -(2x+3y+4z)|_("(2,1,-2)")^("(1,-2,1)")=-1` volt