Find the potential difference `V_(AB)` between `A(2m, 1m, 0)` and `B(0, 2m, 4m)` in an electric field,
`E=(xhati-2yhatj+zhatk)V/m`

Options

A. `2 V`
B. `5 V`
C. `3 V`
D. `4 V`

Answer

C

Explanation

`dV=-E.dr`
`int_B^A dV=-int_(((0,2,4)))^(((2,1,0))) (xhati-2yhatj+zhatk).(dxhati+dyhatj+dzhatk)`
`:. V_A-V_B=-int_(((0,2,4)))^(((2,1,0)))(xdx-2ydy+zdz)`
or `V_(AB)=-[x^2/2-y^2+z^2/2]_(((0,2,4)))^(((2,1,0)))`
When `E.dr` becomes a Perfect Defferential.
Same method is used when `E.dr` becomes a perfect differential. The following example wil illustrate the theory.