A uniform electric field pointing in positive $x$-direction exists in a region. Let $A$ be the origin, $B$ be the point on the $x$-axis at $x = +1\,\mathrm{cm}$ and $C$ be the point on the $y$-axis at $y = +1\,\mathrm{cm}$. Then the potentials at the points $A$, $B$ and $C$ satisfy
A$V_A < V_B$
B$V_A > V_B$
C$V_A < V_C$
D$V_A > V_C$
Answer & Solution
Correct answer: B. $V_A > V_B$
For a uniform electric field in the positive $x$-direction, potential decreases as we move along positive $x$ because $$\vec{E} = -\nabla V.$$ So points with larger $x$-coordinate have lower potential. Here, $A$ has $x=0$, $B$ has $x=1\,\mathrm{cm}$, and $C$ also has $x=0$. Hence $$V_B < V_A$$ and $$V_C = V_A.$$ Now checking the options: only the statement $V_A > V_B$ is correct.
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