Assume that an electric field `vec(E) = 30 x^(2) hat(i)` exists in space. Then the potential differences `V_(A) - V_(0)` where `V_(0)` is the potential at the origin and `V_(A)`, the potential at `x = 2m` is

Options

A. `-80 J`
B. `80 J`
C. `120 J`
D. `-120 J`

Answer

A

Explanation

Given unit in options is wrong.
By using `dv=-vec(E).vec(dx)`
`DV=-int vec(E).vec(dx)`
`V_(A)-V_(0)=-underset(x=0)overset(x=2)(int)30x^(2)dx=-10x^(3)|_(x=0)^(x=2)`
`V_(A)-V_(0)=-10[8-0]=-80 V`