Question

An electric field $ \hat{E}= 30\,x^{2} \hat{i} $ exists in space. Then, the potential difference $ V_A - V_0 $ , where $ V_0 $ is the potential at the origin and $ V_A $ is the potential at $ x = 2\, m $ , is given by

• A. $ -80\, \hat{j} $
• B. $ 120\, \hat{j} $
• C. $ -120\, \hat{j} $
• D. $ 80\, \hat{j} $

Answer 1

Answer: (A)

As we know, the relation between electric field and potential difference is given as
$\int\limits_{v_0}^{v_A} = - \int\limits_{0}^{r} B \cdot dr$
$\Rightarrow V_A - V_0 = - \int\limits _{0}^{2m} 30 x^2 dx $
$ = -30\left[\frac{x^{3}}{3}\right]_{0}^{2}$
$ \Rightarrow V_{A} - V_{0} = -30 \times\left[\frac{2^{3}}{3} - \frac{0}{3}\right]$
$ = -30 \times\frac{8}{3} $
$= -80 V$
Note Potential is a scalar quantity. So, it cannot be written as $- 80\hat{j}$ as given in option.