A potential difference of 4.75 kV is established between parallel plates in air. If the air beco

step 1 In this question, we have two parallel plates that has a potential difference of 4 .75 kilovolts

A potential difference of 4.75 kV is established between...

A potential difference of 4.75 $\mathrm{kV}$ is established between parallel plates in air. If the air becomes ionized (and hence electrically conducting) when the electric field exceeds $3.00 \times 10^{6} \mathrm{V} / \mathrm{m},$ what is the minimum separation the plates can have without ionizing the air?

Key Concepts

Uniform Field Between Parallel Plates

In a system of parallel plates, the electric field is constant if edge effects are neglected. This property simplifies calculations involving potential differences and distances since the relationship E = V/d directly applies.

Electric Field

The electric field is a measure of force per unit charge and is central to understanding the forces that charged particles experience. In parallel plate configurations, the electric field is uniform and is defined as the potential difference between the plates divided by the distance separating them.

Dielectric Breakdown

Dielectric breakdown is the process by which an insulating material, such as air, becomes electrically conductive when the electric field exceeds a critical threshold. This phenomenon is significant in electrical engineering as it sets practical limits for the operating conditions of devices and systems to prevent unwanted ionization.

Relationship Between Potential Difference and Plate Separation

The relationship E = V/d indicates that for a given potential difference, the electric field can be controlled by adjusting the distance between the plates. Maintaining a distance large enough ensures that the electric field remains below the breakdown threshold, thereby preventing ionization of the medium between the plates.

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