In a certain region, a uniform electric field exists in the positive x-direction. Let $V_A = $ potential at $(0,0,0)\text{ cm}$, $V_B = $ potential at $(5,0,0)\text{ cm}$ and $V_C = $ potential at $(0,5,0)\text{ cm}$. The correct relationship between them is:
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Think of electric field lines like a stream flowing downhill. Points at the same "elevation" (perpendicular to flow) have the same potential, while points "downstream" (in the direction of the field) always have lower potential.
Step 1: Understanding the Concept:
There are two key rules for electric potential in a uniform field:
1. Electric potential decreases in the direction of the electric field lines.
2. Potential remains the same at all points on a plane perpendicular to the field lines (Equipotential Surface). Step 2: Analyzing the Points:
The field $\vec{E}$ is along the $+x$ axis.
• Comparing $V_A$ and $V_B$: Point B $(5,0,0)$ is further along the x-direction than point A $(0,0,0)$. Since potential drops in the direction of the field, $V_A > V_B$.
• Comparing $V_A$ and $V_C$: Point A $(0,0,0)$ and point C $(0,5,0)$ have the same $x$-coordinate. They lie on a plane perpendicular to the x-axis. Therefore, $V_A = V_C$.
Step 3: Final Answer:
Combining these, we get $V_A = V_C$ and $V_A > V_B$.
