The electric potetnial in a region along x-axis varies with `x` according to the releation `V(x) = 4 xx 5x^(2)`. Then the incorrect statement is

Options

A. potential difference between th points `x = 1 m` and `x = 2 m` is `15` volt
B. force experienced by a one coulomb charge at `x=-1m` will be `10N`
C. the force experienced by the above charge will be towards `+x`-axis.
D. a unifrom electric field exists in the region along the x-axis.

Answer

D

Explanation

`V(x) = 4 + 5x^(2)`
`V(1) = 4 + 5(1)^(2) = 9 "volt"`
`V(2) = 4 + 5(2)^(2) = 24 "volt"`
Potential difference `= (24 - 9) "volt" = 15 "volt"`
`E = - (dV)/(dx) = -(d)/(dx) [4 + 5x^(2)] = - 10x`
Electric field at `x = 1m = 10 NC^(-1)`
SO, force on `1C` charge is `10N`. It is towards `+x` axis.