Question

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

Answer 1

Correct Answer - C

Answer 2

 \(\vec E=30\, k \hat i\)

\(dv=-\int Edx \)

\(\int\limits _{V_0}^{V_A} dv=-\int \limits_0^2 30x\,dx\)

\(=-\left[\frac{30\,x^2}{2}\right]_0^2 \)

\(=-\left[\frac{30\times {\not4}^2}{\not 2}\right]\)

\(V_A-V_0=-60 V.\)