Question

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

• A. $10\text{V}$
• B. $30\text{V}$
• C. $40\text{V}$
• D. $20\text{V}$

Answer 1

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


$V_A-V_O=-\int E_{x}dx$

$\Rightarrow V_A-10=-$ Area under $E_x-x$ curve

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

$\Rightarrow V_A=20+10=30\text{V}$

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