Final answer:
The minimum separation distance 'd', where sparking would occur in a parallel plate capacitor, is given by the equation d = V/(3.0×10⁶ V/m), where V is the maximum potential difference before sparking.
Step-by-step explanation:
The question pertains to the situation where you have a parallel-plate capacitor and you want to know how close you can place the plates without seeing a spark, that is, without the E field (electric field) exceeding 3.0×10⁶ V/m. The electric field E within a parallel-plate capacitor is given by E = V/d, where V is the voltage (or potential difference) across the plates, and d is the separation distance between the plates. In this case, we want to solve for d to prevent sparking: d = V/E. But the question does not provide the value for V. However, the statement implies that any increase in V would cause a spark, which suggests that the plates are already at a voltage V just under the breakdown voltage for air, which is 3.0×10⁶ V/m.
Therefore, when E = 3.0×10⁶ V/m, this is the maximum electric field, so the potential difference V must be at the maximum safe value just before breakdown. Solving for the plate separation distance d at this point yields d = V/(3.0×10⁶ V/m). Since the question does not provide a specific V, we cannot compute a numerical value for d but rather show how the distance d can generally be determined from the above formula.
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