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

Answer

C

Explanation

Potential difference between any two points inan electric field is given by,
`dV=-barE.bar(dx) int_(V_(O))^(V_(A))dV=-int_(0)^(2)30x^(2)dx`
`V_(A)=V_(O)=-[10x^(3)]_(0)^(2)=-80J//C`