Step 1 (Formula / Governing Law & Given Data): [0.25 Mark]
The electric field $E$ between the plates of a parallel plate capacitor is related to the potential difference $V$ and the separation distance $d$ by the following relation:
$$E = \frac{V}{d}$$Given: The electric field $E$ is constant ($E = \text{constant}$).
Step 2 (Step-by-Step Mathematical Working): [0.5 Mark]
To maintain a constant electric field $E$, we rearrange the formula to express $V$ as a function of $d$:
$$V = E \cdot d$$Since $E$ is a constant, let $E = k$ (where $k$ is a positive constant). The equation becomes:
$$V = k \cdot d$$This equation is in the form of a linear equation $y = mx$, where $y = V$, $x = d$, and the slope $m = E$. This represents a straight line passing through the origin.
Step 3 (Final Concluded Answer): [0.25 Mark]
The graph of $V$ versus $d$ is a straight line passing through the origin with a slope equal to the magnitude of the constant electric field $E$.
💡 EL10 Concept Insight (Easy to Understand):
Think of the electric field like the "steepness" of a hill; if you want the hill to stay just as steep while you pull the plates further apart, you have to keep increasing the height (voltage) proportionally, which creates a straight-line relationship.