An electric field is given by `E_(x) = - 2x^(3) kN//C`. The potetnial of the point `(1, -2)`, if potential of the point `(2, 4)` is taken as zero, is

Options

A. `-7.5 xx 10^(3) V`
B. `7.5 xx 10^(3) V`
C. `-15 xx 10^(3) V`
D. `15 xx 10^(3) V`

Answer

A

Explanation

`dV = - vecE.vecdr = - (-2x^(3)hati).(dxhati + dyhatj + dz hatk) = 2x^(3) dx`
`rArr underset(0)overset(v)int dV = underset(2)overset(1)int (2x^(3)) xx 10^(3) dx`
`V = - 7.5 xx 10^(3) V`