Question

A graph of the $\text{x-}$component of the electric field as a function of $x$ in a region of space is shown. The $\text{y}$ and $\text{z}$ components of the electric field are zero in this region. If the electric potential is $10\text{V}$ at the origin, then potential at $x=2\text{m}$ is

• A. $40\text{V}$
• B. $30\text{V}$
• C. $-10\text{V}$
• D. $10\text{V}$

Answer 1

The correct option is B $30\text{V}$

We know the relation between potential difference and electric field,
$V-V_o=-\int E_{x}dx....\left(1\right)$

Thus, the change in potential is the negative of the area under the $\text{E-x}$curve. Let the potential at $x=2\text{m}$ be $V_A$.


Using equation $\left(1\right)$, and the given graph,

$V_A-V_o$ = - Area of $\Delta \text{OAB}$

$\Rightarrow V_A-10=-\frac{1}{2}\times \left(\text{OB}\right)\times \left(\text{BA}\right)$

$\Rightarrow V_A-10=\frac{1}{2}\times 2\times (-20)$

$\Rightarrow V_A=20+10$

$\therefore V_A=30\text{V}$

Hence, option (d) is the correct answer.