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

Options

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

Answer

A

Explanation

`dV = - vec(E). Vec(dx) = -30 x^(2) hat(i). Dx hat(i) = -30 x^(2) dx`
`int_(V_(0))^(V_(A)) dV = -int_(0)^(2) 30 x^(2) dx`
`V_(A) - V_(0) = -[10x^(3)]_(0)^(2) = -80 V`